Research Article

Evolutionary Biology

Tradeoff breaking as a model of evolutionary transitions in individuality and limits of the fitness-decoupling metaphor

Philosophy Department, Macquarie University, Australia
Department of Philosophy & Charles Perkins Centre, The University of Sydney, Australia
Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Germany
Centre d'Écologie Fonctionnelle et Évolutive (CEFE), CNRS, France
Laboratoire Biophysique et Évolution, CBI, ESPCI Paris, Université PSL, CNRS 75005 Paris, France, France
Department of Microbial Population Biology, Max Planck Institute for Evolutionary Biology, Germany
Institute of Microbiology, Kiel University, Germany

Aug 17, 2022

https://doi.org/10.7554/eLife.73715

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Accepted for publication after peer review and revision.

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Version of Record published: September 13, 2022 (This version)
Accepted Manuscript published: August 17, 2022 (Go to version)
Accepted: June 28, 2022
Received: September 8, 2021
Preprint posted: September 2, 2021 (Go to version)

1. Of interest
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Research Article Updated Jun 1, 2023
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Introduction
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Abstract

Evolutionary transitions in individuality (ETIs) involve the formation of Darwinian collectives from Darwinian particles. The transition from cells to multicellular life is a prime example. During an ETI, collectives become units of selection in their own right. However, the underlying processes are poorly understood. One observation used to identify the completion of an ETI is an increase in collective-level performance accompanied by a decrease in particle-level performance, for example measured by growth rate. This seemingly counterintuitive dynamic has been referred to as fitness decoupling and has been used to interpret both models and experimental data. Extending and unifying results from the literature, we show that fitness of particles and collectives can never decouple because calculations of fitness performed over appropriate and equivalent time intervals are necessarily the same provided the population reaches a stable collective size distribution. By way of solution, we draw attention to the value of mechanistic approaches that emphasise traits, and tradeoffs among traits, as opposed to fitness. This trait-based approach is sufficient to capture dynamics that underpin evolutionary transitions. In addition, drawing upon both experimental and theoretical studies, we show that while early stages of transitions might often involve tradeoffs among particle traits, later—and critical—stages are likely to involve the rupture of such tradeoffs. Thus, when observed in the context of ETIs, tradeoff-breaking events stand as a useful marker of these transitions.

Editor's evaluation

This article makes two important, independent contributions to the multicellularity/major transitions literature. First, it sheds light on the concept of ‘fitness decoupling’, providing a strong mathematical foundation for the claim that the fitnesses of cells and groups cannot be formally decoupled during an evolutionary transition in individuality. Second, the article proposes using the evolution of tradeoff-breaking traits as an indication that an evolutionary transition has occurred. This dovetails well with existing fitness-based approaches, extending the toolkit of those studying major evolutionary transitions.

https://doi.org/10.7554/eLife.73715.sa0

Introduction

Evolutionary transitions in individuality (ETIs) are events of major significance in the history of life. They begin with lower-level entities (particles) and complete when higher-level entities (collectives) acquire properties sufficient to participate directly in the process of evolution by natural selection (see Appendix 1, ‘Glossary’ for definitions of technical terms). ETIs of particular note include the evolution of chromosomes (from genes), the eukaryotic cell (from an ancestral eubacterium and archaebacterium), and multicellularity (from single cells) (Buss, 1987; Jablonka, 1994; Maynard Smith and Szathmáry, 1995; Michod, 1999a; Bourke, 2011; Calcott and Sterelny, 2011; Bouchard and Huneman, 2013; West et al., 2015; van Gestel and Tarnita, 2017). Here, we focus attention on the transition from cells to multicellular life.

Evolutionary dynamics underpinning the transition to multicellularity have proven difficult to capture; however, influential for theory—and guiding experimental analysis—has been the concept of ‘fitness decoupling’, which posits that the fitness of a collective in the early stage of a transition is directly proportional to the fitness of its particles and that, as the evolutionary transition proceeds, collective fitness ‘becomes decoupled from the fitness of its lower-level components’ (Michod and Nedelcu, 2003, p. 96). This notion is based on the fact that the evolution of cooperation, division of labour, or conflict-mediating mechanisms seems to improve collective-level fitness at the cost of particle-level fitness. This phenomenon has been interpreted through the lens of an export-of-fitness framework, in which the evolution of such mechanisms marks ‘transfer of fitness’ from particle to collective levels (Michod and Roze, 1999b; Michod and Nedelcu, 2003; Michod, 2005; Okasha, 2006; Michod et al., 2006b; Okasha, 2009; Folse and Roughgarden, 2010; Michod et al., 2003; Shelton and Michod, 2020; Michod, 2022; Doulcier et al., 2022).

In recognising challenges associated with assigning fitness to particles, as opposed to collectives, and building from earlier work (e.g., Michod, 2005; Michod, 2006a), Shelton and Michod, 2014 proposed the idea of ‘counterfactual fitness’. They defined the counterfactual fitness of a collective as the fitness that this collective would have if there were no collective-dependent effects on the interactions of particles within the collective. This approach can be regarded as a way of apportioning fitness components to different levels: the counterfactual component corresponds to the particle level, while the collective-dependent effects correspond to the collective level. Counterfactual fitness was later integrated in the fitness decoupling, fitness transfer or export-of-fitness framework (explicitly in Shelton and Michod, 2020, but see Michod, 2005; Michod, 2006a, for the precursor of this idea). Accordingly, fitness decoupling is seen to have occurred when the collective-level-dependent component of fitness increases and the counterfactual component goes to zero. While useful, in that the idea of counterfactual fitness permits accounting for the functional integration or mutual interdependence of the particles within an entity, which is an important characteristic of an individual (see Godfrey-Smith, 2009), its use in the context of fitness decoupling leaves unresolved the mechanism by which fitness at one level can be exported to the other. A primary goal of this article is to add clarity to these discussions.

Although the idea of fitness transfer or decoupling, whether understood literally or counterfactually, seems to be intuitive, and empirical tests straightforward, it has been suggested that this might not be the case. The notion of fitness and its use in evolutionary thinking is generally problematic (as pointed out, among others, by Doebeli et al., 2017). In addition, actual particle and collective fitness are often ‘mathematically equivalent ways of bookkeeping’ (as pointed out by Shelton and Michod, 2014, p. 457, in the context of their model). Further, measurement of fitness in experiments—particularly in the context of ETIs, where fitness is usually compared between two organisational levels—is difficult (Bourrat, 2015a; Bourrat, 2015b; Bourrat, 2021a; Bourrat, 2021b). Experimental investigations of early stages in the transition to multicellularity (Hammerschmidt et al., 2014; Rose et al., 2020) are a good example thereof. Data from these experiments showed collective-level fitness to have improved while cell-level fitness declined over evolutionary time, giving the impression that the fitness of cells had decoupled from the fitness of collectives (see below for details). Although several proxies for fitness were obtained, such as maximum growth rate and competitive fitness (as is traditionally done in the field, see Lenski et al., 1991; Wiser et al., 2013; Wiser et al., 2015), for practical reasons, it was impossible to measure cell and collective fitness over the same timescale, which would have been required for a meaningful comparison (see Box 1). The notion of counterfactual fitness is also difficult to operationalise as no consensus method for its measure has emerged from the literature. The relevance of various proxies that could be used, such as measuring fitness in a modified environment that prevents the formation of collectives (e.g., by shaking the culture medium) or measuring the fitness of genetically engineered mutants unable to form collectives (revertant for the collective-formation mutations), is yet to be assessed.

Box 1

Comparing fitnesses.

Determining whether the fitness of an entity is higher or lower than that of another entity requires obtaining commensurate fitness estimates for the two entities. In this box, we consider monomorphic lineages; thus, ‘individual’ or ‘lineage’ fitness can be used interchangeably.

A conventional fitness estimate is an entity’s expected number of offspring after one generation. However, for this estimate to be adequate for the purpose of comparison, the generation time of the entities compared must be the same. If they are not, a different/same number of offspring per generation does not necessarily indicate a different/same fitness value. To see this point, suppose two entities A and B, which double at each generation, such as two strains of bacteria. Everything else being equal, A doubles at a faster rate than B because it has a shorter generation time. Over the same absolute period, A will have a higher number of descendants than B, and one could infer that A is fitter than B. Box 1—figures 1a and 1b illustrate the situations, respectively, where a fitness comparison is made based on generational (and, thus, invalid) and absolute times (valid).

A more appropriate measure for the purpose of fitness comparison when generation times differ between the focal entities is the long-term growth rate of the population or the Malthusian parameter. These values are often computed from empirical actuarial tables using population projection models (see Caswell, 1989) or the repeated census of the population (e.g., in microbiology).

However, long-term growth rates can only be compared if they are made over the same set of events. Any observation where one entity appears fitter than the other, but for which a different set of events has been used (different timescale or different environment), could in reality be one where there is no difference between the two. In other words, it could be a spurious observation.

To take an example where the two environments, rather than the times over which reproductive outputs are measured, are different, consider two identical plants receiving different quantities of resources. The plant receiving more resources produces more seeds. Yet, this difference in reproductive output cannot lead to the conclusion that these two plants have different fitnesses where ‘fitness’ is associated with natural selection. In our example, because the two plants are initially identical, they necessarily have the same fitness. This situation is depicted in Box 1—figure 1c and d. In Box 1—figure 1c, the fitnesses are compared in two different environments—and, thus, the comparison is invalid—while in Box 1—figure 1d, the comparison is made in the same environment.

In some situations where one wants to make fitness comparisons, the environment presents fluctuations in time. In this case too, to be comparable, they must refer to the same set of events. For instance, if A is in environment 1, and B is successively in environments 1 and 2, the two resulting fitness values are not comparable because they do not inform one of the potential outcomes of competition in environment 1, in environment 2, or in a temporal succession of the two. This invalid comparison is represented in Box 1—figure 1e. Therefore, a condition for comparison, taking into account environmental change, is that the two organisms follow the same temporal succession of environments, as presented in Box 1—figure 1f. Note, crucially, that we assume here that whether an entity is in a given environment is independent of its type. If a dependence of the environment on the type exists, this environment effectively becomes an extended phenotype (Lu and Bourrat, 2018).

If the environmental changes are not deterministic, a weaker condition than the same temporal succession of environments is that the two organisms experience the same distribution of environments and transition probabilities between environments (steady-state) (see Doulcier et al., 2021). This type of scenario is not discussed in the main text (but see Box 3).

Box 1—figure 1

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Valid fitness comparisons require measures over the same set of events (same environment and timescale).

Invalid comparisons: (**a, c, e**). Valid comparisons: (**b, d, f**).

Building on this experimental approach and philosophical insights about valid fitness comparisons between levels of organisation from Bourrat, 2015a and Bourrat, 2015b, Black et al., 2020 constructed a simple ‘ecological scaffolding’ model that showed how a minimal set of ecological conditions can produce evolutionary dynamics where particle and collective fitness appear ‘decoupled’. Population structure creates a tradeoff between short-term growth through particle division and long-term growth through collective persistence. This led Black et al. to conclude that a ‘fitness decoupling’ observation can be explained in terms of a reduction of short-term particle growth rate coinciding with increased collective-level performance (over a longer timescale), rather than in terms of transfer of fitness between particles and collectives. If it is true that the fitness of cells and collectives cannot decouple, where does this leave our understanding of dynamic processes that underpin ETIs? The mechanistic approach with an ecological focus is one route (see Black et al., 2020; Bourrat, 2022; Doulcier et al., 2020), as is the ratcheting-mutation model proposed by Libby et al., 2016. However, there is also a need to identify hallmarks of transitions that might allow identification and experimental validation of ETIs.

We begin by elaborating on the notion of ‘fitness decoupling’ and related concepts such as ‘export of fitness’ and ‘fitness transfer’, showing how this idea has been used in both the theoretical and experimental literature (Section 1). In Section 2, we present a population projection model of an abstract proto-multicellular organism and show that particle and collective fitness are necessarily equal for all structured population dynamics models that reach a stable collective size distribution, generalising and unifying results from the literature (e.g., Shelton and Michod, 2014; Bourrat, 2015a; Bourrat, 2015b, Bourrat, 2021a; Black et al., 2020). In Section 3, we show that the intuited dynamics of transitions are captured best by the language of traits and tradeoffs among traits. Finally, we turn to the challenge of defining essential features of ETIs and argue that events that break the tradeoff constraining the ancestral particle—hereafter referred to as ‘tradeoff breaking’—stand as a marker of an ETI (Sections 4 and 5).

Results

1. Challenges arising from the application of fitness-centred approaches to the study of ETIs

One classical way to characterise particle fitness is to measure long-term reproductive success under a given set of environmental conditions relative to other particles (Pence and Ramsey, 2013; Doulcier et al., 2021). In a more practical sense, fitness is often measured as a per capita growth rate—that is, the average number of offspring produced by an individual per unit of time (or per generation) (Fisher, 1930; Metz et al., 1992). Whenever a nested system (composed of particles assembled into collectives) is studied, it is possible to measure at least two kinds of ‘fitnesses’: the fitness of particles and that of collectives. To do so, population growth is tallied at each level.

Proponents of the export-of-fitness model and the concept of fitness decoupling argue that during an ETI, the fitness of particles and collectives of particles become ‘decoupled’ (Michod and Roze, 1999b; Michod and Nedelcu, 2003; Michod, 2005; Shelton and Michod, 2009; Hanschen et al., 2015; Hanschen et al., 2017; Shelton and Michod, 2020; Davison and Michod, 2021). More precisely, the two values are predicted not to change in the same way and even to change in different directions: collective-level fitness increases while particle-level fitness decreases (Hanschen et al., 2017). Note that they are not expected to necessarily become independent from one another. All that is required for them to become decoupled is that they are anticorrelated or even less correlated. In some stricter formulations of the concept, collective and particle fitnesses are said to be decoupled as soon as collective fitness is not proportional to the average fitness of its component particles (Michod and Nedelcu, 2003; Okasha, 2006). In this section, we review the theoretical and empirical arguments leading to this prediction.

The idea of fitness decoupling can be traced back to the study of the disruption of higher-level entities by the proliferation of lower-level entities composing them (see Maynard Smith and Szathmáry, 1995, pp. 7–8). If selection acts at two levels during an ETI, why would selection at the lower level (on molecules, cells, or organisms) not disrupt the effect of selection at the higher level (on chromosomes, multicellular organisms, or insect colonies)? Such ‘conflicts’ pose a challenge for integration at the higher level. This phenomenon is present at all organismal levels. For instance, cancerous cells proliferating at a higher rate than healthy cells pose a threat to organismal integrity (Merlo et al., 2006). Similarly, without suppression from the queen, egg-laying worker bees pose a threat to the integrity of the hive (Amdam and Page, 2010). Other examples include selfish genetic elements, which can sometimes produce harmful effects at the organism level (see Werren, 2011, for a review). As a consequence, one may prima facie expect evolutionary trajectories to be the result of opposing processes that would be both a hallmark and a significant hurdle for ETIs.

The idea of fitness decoupling was introduced by Michod and Nedelcu, 2003 (pp. 66–67), to describe the ways conflicts between the higher and lower levels of organisation can be resolved during an ETI: “as the evolutionary transition proceeds, group fitness becomes decoupled from the fitness of its lower-level components […] This transfer and reorganization of fitness components from lower to higher-levels occurs through the evolution of cooperation and mediators of conflict that restrict the opportunity for within-group change and enhance the opportunity for between-group change.” More generally, Hanschen et al., 2017 note that “any trait that is costly at the lower level but beneﬁcial at the group level enhances the ﬁtness of the group at the expense of lower-level ﬁtness and may therefore contribute to ﬁtness decoupling and the emergence of indivisibility of the group”. Okasha and Michod recast the notion of fitness decoupling in the multilevel selection 1/multilevel selection 2 (MLS1/MLS2) framework (Michod, 2005; Michod and Nedelcu, 2003; Okasha, 2006, p. 232). Okasha describes collective fitness during the three stages of an evolutionary transition (Okasha, 2006, p. 238): in the first stage, collective fitness is defined as average particle fitness (MLS1); second, collective fitness is defined as proportional to average particle fitness; finally, gradual decoupling occurs in the transition towards the third stage, where collective fitness is no longer proportional to particle fitness (MLS2). In the export-of-fitness framework of ETIs, collectives initially ‘lack’ individuality (fitness of particles and collectives are proportional) and ‘gain’ individuality once their fitness is ‘transferred’ from the underlying particles (Michod and Roze, 1999b; Okasha, 2006, pp. 234–235).

The concept of fitness decoupling has been regarded as one indicator for the ETI from cells to multicellular individuals (Rainey and Kerr, 2010; Pichugin, 2015; Hanschen et al., 2015; Conlin et al., 2019). In a study using experimental bacterial (Pseudomonas fluorescens) populations, Hammerschmidt et al., 2014 and Rose et al., 2020 propagated collectives over multiple generations, and then asked whether predicted increases in collective-level fitness were realised. This was achieved by competing derived collectives against ancestral collectives over the time frame of a single life cycle generation—the number of offspring collectives left over this period was greater in the derived populations (Figure 1a). Next, they sought understanding of cell-level fitness effects. Ideally, such assays would have been performed over an entire collective-level life cycle; however, for practical reasons, this is nigh impossible. Instead, various cell-level assays were conducted, including assessment of competitive ability in broth culture for the duration of part of the life cycle. Data from these experiments showed cell-level fitness to have declined in derived populations (Figure 1b), at least for the regime where lineages passaged through soma-like and germ-like phases, giving the impression that the fitness of cells had decoupled from the fitness of collectives (Figure 1).

Figure 1

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Fitness-decoupling observation in the *Pseudomonas* system.

Comparison of collective-level persistence (measured as the proportion of collective persistence after one generation when competed against an ancestral reference strain) and cell (particle) fitness (measured as the number of cells comprising a collective) for ancestral (blue) and derived (orange) populations under a regime designed to promote an evolutionary transition in individuality. Error bars represent standard errors of the mean (based on n = 15 ancestral and n = 14 derived lineages, respectively). Redrawn from Hammerschmidt et al., 2014 (Fig. 2), for ease of comparison with Figure 5. Protocol described and statistical analysis performed in Hammerschmidt et al., 2014, showing statistical significance between ancestral and derived collective persistence/cell fitness. Dataset published as Rose et al., 2018.

Measures of cell and collective fitness must derive from analyses performed in the same reference environment and over precisely the same timescale (detailed in Section 2 and Box 1). In the example of Figure 1, collective fitness is computed by considering a full collective generation, while particle fitness is computed within collective development. This renders the comparison spurious, as illustrated in Figure 2. Computing the fitnesses at the same timescale and, thus, in the same reference environment would involve simultaneously tallying the increase of individual cells and number of collectives in a time frame spanning several collective cycles.

Figure 2

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Collective and particle fitnesses are not measured over the same environment.

During an evolutionary transition in individuality, there are two levels of organisation: collectives (blue triangles) are composed of particles (orange disks). Both levels have their own genealogy (black arrows). Collective fitness is computed by considering one or several full collective generations (purple timeline), while particle fitness is computed within each collective development (grey timeline). As a result, they may exhibit opposing dynamics (increasing for collective and decreasing for particle fitness), giving rise to the fitness-decoupling observation.

The export-of-fitness account has been refined by Shelton and Michod, 2020 in light of the counterfactual approach to the evolution of multicellularity they developed earlier (Shelton and Michod, 2014). Following this account, decoupling and/or transfer occur not simply from the particle-level to the collective-level fitness, but between the counterfactual particle level (i.e., particles as they would be if they were not part of the collective) and the collective level (Shelton and Michod, 2020). This interpretation alleviates some of the ambiguities present in earlier work by explicitly stating a point that was previously open to interpretation. However, we suggest that it is incompatible with the use of the notion of export of fitness. This is so because the vocabulary suggests that transfer actually occurs between actual and counterfactual quantities, the latter of which do not actually exist by definition.

To summarise, there are two ways in which the export of fitness has been used in the literature: first as a transfer between actual quantities, and second as a process concerning counterfactual quantities (note that since Shelton and Michod, 2020, the original authors have explicitly favoured the second interpretation). We suggest that neither account is satisfactory—actual export of fitness is impossible because actual cell and collective fitness are equal, and counterfactual export of fitness is inconsistent because there is no material quantity to be transferred. The first point has significant support within the literature (Shelton and Michod, 2014; Bourrat, 2015a; Bourrat, 2015b) and can be proved for a large class of population dynamics models (as we do in Section 2). The second point is more contentious; however, it primarily concerns the limits of the notion of export of fitness rather than the use of the counterfactual method to study ETIs and detect tradeoffs. In light of these two points, we distinguish between, on the one hand, the notions of ‘fitness decoupling’, ‘fitness transfer’, and ‘export of fitness’, and, on the other, ‘fitness-decoupling observations’ (see Appendix 1, ‘Glossary’). Consequently, we have no objection to the use of fitness-decoupling observations in the context of ETIs. To clarify this discussion, Sections 3–5 build upon Section 2 to unfold a general trait-based adaptive scenario of ETIs that is compatible with both experimental fitness-decoupling observations (that stem from a tradeoff) and their deviations.

2. Commensurably computed particle and collective fitness are equal

In this section, we present a population projection model (Leslie, 1945; Caswell, 1989) of an abstract proto-multicellular organism. The population is divided into classes corresponding to different sizes of collectives, as is commonly done in the literature (Tarnita et al., 2013; Pichugin et al., 2017). We define collective fitness in the context of this model (Section 2.2) and illustrate the different conventions that can be used to define particle fitness (Section 2.3). We provide proof that, under minimal conditions, if particle and collective fitness are computed with respect to the same set of events (i.e., in the same reference environment), they are equal (Section 2.3). Finally, we use this result to clarify conditions under which fitness-decoupling observations can be made (Section 2.4). Significantly, this model assumes that particles and collectives can coexist. In other words, we do not model the potential competition between particles and collectives, as done by Tarnita et al., 2013. Also, we do not study the problem posed by the existence of free-riders or cheaters in collectives. However, this could be done by adding a game-theoretic layer to our model.

2.1 Modelling a nested demography

Consider a population of genetically homogeneous particles, structured into collectives following the life cycle illustrated in Figure 3. Each collective is characterised by its size—that is, the number of particles it comprises. At each time step, a proportion $γ_{i}$ of collectives of size class i increases to size class $i + 1$ , a proportion $μ_{i}$ shrinks to size class $i - 1$ , a proportion $δ_{i}$ dies, and the remaining collectives (i.e., a proportion $α_{i} = 1 - δ_{i} - μ_{i} - γ_{i}$ ) stay the same size. Let $N$ be the maximum size above which collectives cannot grow. Here, the collectives are voluntarily abstract because the statement the model supports is quite general, but one can consider that the particles are cells and growth and shrinkage of the collective is mediated by cell duplication and death. Additionally, collectives reproduce: a collective of size $i$ produces on average $β_{i}$ propagules of size class 1 at each time step. Such a life cycle can be represented as a population projection model, whose dynamics are given by

c_{i} (t + 1) = \sum_{j = 1}^{N} a_{i j} c_{j} (t),

where $c_{i} (t)$ is the density of collectives of size $i$ at time $t$ , and $a_{i j}$ is the weight of the $i \to j$ edge of the life cycle graph (Figure 3; the $a_{i j}$ are the elements of the population projection matrix $A$ ) for all values of $i$ and $j$ between 1 and $N$ . It follows that the population density of particles is given by

n (t) = \sum_{j = 1}^{N} k_{j} c_{j} (t),

where $n (t)$ is the number of particles within the population at time $t$ , and $k_{j}$ the number of particles corresponding to size class $j$ . For instance, if we consider that all particles reproduce once for the collective to grow one size class, then $k_{j} = 2^{j - 1}$ .

Figure 3

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Life cycle of collectives as a size–class population projection model.

Circles represent a size class of collectives; arrows represent the flow of individuals between size classes. At each time step, collectives of size class i can grow (if i < N), shrink, or stay the same size. They also leave propagules of size class 1. See main text for details.

2.2 Computing collective fitness

We define the fitness of collectives as the Malthusian parameter or asymptotic exponential growth rate of a population of collectives sharing the same trait value (Metz et al., 1992). If all transitions represented in the life cycle graph are possible—that is, $0 < α_{i} < 1 \forall i = 1, 2, . . ., N - 1,$ as well as $β_{i} > 0 \forall i = 1, 2, . . ., N - 1$ —then the matrix $A = {(a_{i j})}_{i, j \in [1, 2 \dots N]}$ is non-negative and primitive. Following the Perron-Frobenius theorem (see Caswell, 1989, p. 57), there exists a positive eigenvalue of $A$ , noted $λ$ , called the dominant eigenvalue of $A$ , with an associated non-negative eigenvector $w$ . Moreover, the strong ergodic theorem (see Caswell, 1989, p.57) shows that the long-term dynamics of the population are described by a growth rate and a stable population structure $w$ . When these assumptions are met, the fitness of collectives is given by:

F = \underset{t \to \infty}{l i m} (\frac{l n (\sum_{j = 1}^{N} c_{j} (t)) - l n (\sum_{j = 1}^{N} c_{j} (0))}{t}) = l n (λ)

where the first equality is given by the definition of fitness, the second by the Perron–Frobenius and strong ergodic theorems, and $c_{j} (t)$ is the density of collectives of size class at time $t$ .

2.3 Computing particle fitness

In contrast to collective fitness, computing particle fitness is more challenging. There are, prima facie, at least three ways to compute the fitness of a particle. Each gives rise to a different measure that we will call $f_{1}$ , $f_{2}$ , and $f_{3}$ (illustrated in Figure 4; their expression for the current model will be given later). To compute:

$f_{1}$ , look within each collective and consider the dynamics of the particles. This is equivalent to ignoring all the ‘between collective’ level events (collective births and deaths). This is what is done experimentally when measuring cell density within isolated collectives (Figure 1, Hammerschmidt et al., 2014).
$f_{2}$ , look at a theoretical monoparticle collective. This is equivalent to ignoring all the ‘within collective’ events (collective growth and shrinking). This conception of fitness corresponds to the notion of ‘counterfactual fitness’ proposed by Shelton and Michod, 2014; Shelton and Michod, 2020 because it is equivalent to the fitness that particles would have if they were genetically equivalent (same trait values), but without the ability to produce multiparticle collectives. This is also close to the experimental measurements of cell density performed experimentally (Hammerschmidt et al., 2014; ‘growth rate’ in ED Figure 4) under conditions preventing the formation of collectives (shaking).
$f_{3}$ , take into account all events (i.e., within and between collective), with counts of the number of particles through time.

Figure 4

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Three ways to compute particle fitness ( $f_{1}$ , $f_{2}$ , and $f_{3}$ ) in a lineage starting from a single particle.

Top: each solid horizontal line represents the life span of a particle. The vertical axis has no unit and only represents population structure. Particles within the same collectives are represented as a series of horizontal lines close to one another (isolated particles count as monoparticle collectives). Each dashed vertical line connects a parental collective to its offspring (which starts as a single cell). Greyed-out elements for $f_{1}$ and $f_{2}$ indicate the processes that are omitted during the fitness calculation. Bottom: the time series below each example shows how particles are tallied. In the case of $f_{1}$ , between-collective events are ignored. Thus, the two particles are the only ones relevant for its computation, whereas, in the case of $f_{2}$ , within-collective birth–deaths and their effects are ignored. Thus, the three particles (i.e., monoparticle collectives) are relevant for its computation. Finally, in the case of $f_{3}$ , the full lineage is used. Thus, all six particles must be taken into account for its computation.

Each of these ways to compute fitness uses a different reference environment (including the timescale). Each can be adequate in different contexts. It is appropriate to measure particle fitness considering within-collective events ( $f_{1}$ ) only when the evolutionary process studied occurs in the short term. For instance, computing $f_{1}$ can tell us which mutant cell lineage can take over within an organism (e.g., cancerous lineages). The counterfactual method $f_{2}$ gives information about a ‘what if’ world where particles cannot be organised in collectives (i.e., in the model, collectives cannot grow: $γ_{i} = 0$ ). It might give information on the unicellular ancestor of a collective. Indeed, a reasonable hypothesis is that the ancestral trait values are those that maximise counterfactual fitness (Shelton and Michod, 2020, p. 8).

However, there is no a priori reason for the values of $f_{1}$ , $f_{2}$ , and $f_{3}$ to be equal to each other, or even to change in the same direction when the traits of the organism change. This is clear in view of their expression in the model. Considering within-collective dynamics (ignoring the effect of density dependence, as is usually done in experiments) gives $f_{1} = \ln (1 - μ_{1} + (k_{2} - 1) γ_{1})$ . (That is, the expected exponential growth rate of a discrete-time branching process (or Bienaymé–Galton–Watson process) where each individual leaves either 0, 1, or $k_{2}$ offspring with probabilities $μ_{1}$ , $(1 - μ_{1}) (1 - g_{1})$ , and $(1 - μ_{1}) g_{1}$ , respectively.) In contrast, considering the counterfactual collective dynamics gives $f_{2} = \ln (1 - δ_{1} + β_{1})$ . Comparing the two equations, we can see that $f_{2}$ does not depend on $γ$ . It follows that an increase in $γ$ would result in an increase in $f_{1}$ with no consequence for $f_{2}$ . Mutatis mutandis, the same applies for $μ$ , $δ$ , and $β$ .

The case of $f_{3}$ is different. The expression of $f_{3}$ is given by the long-term exponential growth rate of $n$ , which is a linear combination of exponentially growing terms $k_{i} c_{i} (t)$ and, thus, asymptotically grows at the rate of its largest coefficient. By definition, this coefficient is $λ$ , the dominant eigenvalue of $A$ . Intuitively, this means that once the population has reached a stable size distribution, the relative proportion of different collective sizes does not matter for computing the overall growth rate of particles—they grow at the same rate as the collective population. Thus, $f_{3} = \ln (λ) = F$ . It follows that a change in $γ$ (or $μ$ , $δ$ , and $β$ ) would affect $f_{3}$ and $F$ in the same way. This shows that when the particle fitness is computed with the same frame of reference (i.e., the same environment) as collective fitness (using the same timescale and the same set of events), the values are (mathematically) equal.

2.4 Counterfactual fitness-decoupling observations can be useful to detect tradeoffs

With these distinctions in place and the constraint that, to be compared, fitnesses must be measured over the same set of events (i.e., same environment over the same timescale; see Box 1 and Section 1), the apparent contradiction of a simultaneous increase in collective fitness and decrease in particle fitness of a single biological entity is dissolved. More precisely, either fitness at the particle level and the collective level are commensurably computed—that is, with respect to the same biological object and in the same reference environment—in which case they are equal ( $F$ and $f_{3}$ ), or they refer to different biological settings ( $f_{1}$ or $f_{2}$ and $F$ ) and, thus, the biological significance of their differential dynamics is not immediately clear.

While these points have been made in the literature (see Section 1), our mathematical proof applies to a larger class of population dynamics models—it is not tied to an MLS1/MLS2 framework and does not require any assumptions regarding the relationship between particle and collective life history traits, such as the usual assumption that collective viability is a linear function of individual viability (since the $γ, μ, δ, β$ are free). It only requires that the population reaches a stable size distribution; only if collectives are able to grow (or shrink) indefinitely, which is not a realistic assumption for ETIs, could genuine fitness decoupling be observed (see Bourrat, 2021a, Chapter 5 for details).

Although observations that $f_{1}$ or $f_{2}$ decrease over time do little to clarify the process of an ETI—a point to which we return in Section 3.3—such observations can be understood as a consequence of an underlying tradeoff and could, thus, prove useful in their experimental assessment. In the next section, we introduce a model of such a tradeoff that provides a plausible biological mechanism for the emergence of multicellular collectives under given conditions, while displaying a simultaneous increase in $F$ and a decrease in $f_{2}$ . However, tradeoffs leading to this observation might not exist or be detected in all ETIs. We present such a biological scenario in Section 5.

3. Tradeoffs between particle traits drive ETIs

The previous section showed that if collective and particle fitness are computed in the same reference environment, they are necessarily equal. In addition, it showed that a fitness-decoupling observation (e.g., $f_{2}$ and $F$ going in different directions) offers little information about the mechanism of ETIs on its own since there is no reason to relate the dynamics of $f_{1}$ or $f_{2}$ to that of collective fitness $F$ without additional assumptions about the system (i.e., that ancestral particles and particles within the collective are restricted to the same subset of the trait space, e.g., by a tradeoff). In this section, we present an evolutionary model of ETIs that includes these additional assumptions (Section 3.1), describe under which conditions fitness-decoupling observations can occur (Section 3.2), and provide an example involving a tradeoff between two traits: the survival of existing collectives and the production of new cells (Section 3.3). This example features an increase of F and a decrease of $f_{2}$ along the evolutionary trajectory. We focus on $f_{2}$ because it is more relevant to ETIs; while $f_{1}$ has been discussed more strictly in the levels of selection literature, $f_{2}$ can be interpreted as the hypothetical fitness an ancestor cell would have (Shelton and Michod, 2020). Nonetheless, the same argument could be made for $f_{1}$ .

3.1 Modelling evolution

The demographic model of Section 2 is completed with a model of evolution in two steps. First, consider that the life cycle of collectives (summarised by the population projection matrix $A$ ) depends upon a trait $θ \in [0, 1]$ whose value can change by mutation. We consider here mutations to be abstract phenotypic changes—the mechanism by which they are produced could be either phenotypic plasticity, environmental change, or actual genetic mutations. For each trait value $θ$ , a corresponding fitness value $F (θ)$ exists. Second, we use the simplifying assumptions of Lande’s Equation (Caswell, 1989, p. 164)—namely, the separation of demographic and evolutionary timescales—and the absence of density-dependent effects, and perform a successive-invasion analysis. These assumptions lead to the following equation for the evolution of the average trait value $\bar{p}$ in the population:

\frac{d \bar{θ}}{d t} = σ_{θ} F (\bar{θ})^{- 1} {\frac{d F}{d θ} |}_{(θ = \bar{θ})},

where $σ_{θ} > 0$ is the variance of mutation effects on the trait $θ$ . As a consequence, the model predicts that the average value of the trait $\bar{θ}$ will ‘climb up’ the fitness gradient $\frac{d F}{d θ}$ as fitter mutants emerge and invade the population.

The ancestral phenotype (i.e., the initial condition $\bar{θ} (t = 0)$ of the evolutionary trajectory) will be taken to be $θ_{0}$ , the optimal trait value for the ancestral unicellular organism. Thus, $θ_{0} = \arg max_{θ} f_{2} (θ)$ , where $f_{2} (θ)$ is the value of $f_{2}$ for an organism with trait $θ$ . Similarly, let $θ^{*}$ be the optimal trait value for the collective, where $θ^{*} = \arg max_{θ} F (θ)$ . The code implementing this model and drawing the figures presented here is available as supplementary material (doi: 10.5281/zenodo.5352208). It uses the Matpopmod library (Bienvenu and Doulcier, 2021).

3.2 Conditions for fitness-decoupling observations between $f_{1}$ or $f_{2}$ and $F$

Once a mutation (or change in the environment) makes the first multiparticle collective possible, the process that drives population dynamics is one associated with $F$ . A sufficient condition for fitness-decoupling observations to be possible would be that the trait values that are optimal for monoparticle collectives ( $θ_{0}$ ) are not optimal for multiparticle collectives ( $θ^{*} \neq θ_{0}$ ), provided the fitness landscape is sufficiently smooth (and both $F$ and $f_{2}$ are continuous functions of θ with a single maximum value). Thus, as selection acts during the ETI and drives the trait values towards fitter collectives (towards $θ^{*}$ , the optimal value of $θ$ for $F$ ), this would necessarily lead to less fit ‘counterfactual’ monoparticle collectives (away from $θ_{0}$ , the optimal value for $f_{2}$ ). Conversely, a sufficient condition to observe ‘coupling’ between $f_{2}$ and $f_{3}$ (or $F$ ) would be that the optimal trait values for these two measures coincide ( $θ^{*} = θ_{0}$ ) and that the ancestral trait was not optimal. In such a condition, the evolutionary trajectory of the population would tend towards traits with a higher value of $F$ and, coincidently, towards higher values of $f_{2}$ (hence the existence of a ‘coupling’).

3.3 An example: The tradeoff between collective growth and persistence

Let $θ \in [0, 1]$ be a trait that controls the relative investment of the particles towards collective survival and collective growth, modelled by parameters $s$ and $b$ , such that $s = θ$ and $b = 1 - θ$ . More precisely, let the probability for a collective of size class $i$ to survive a single time step be $p_{i}$ , with $p_{1} \in [0, 1]$ and for $i = 2, \dots, N$ , $p_{i} = 1 - e^{- η s}$ (where $η$ is a scaling factor). Let the probability for a collective of size class $i$ to grow to the next class size during a time step be $g_{i}$ , with $g_{i} = 1 - e^{- η b}$ for $i = 1, \dots, N - 1$ and $g_{N} = 0$ . Additionally, let the expected number of propagules shed by a collective of class size $i$ be $m_{i} = η b k_{i}$ . Thus, following the Birth-Flow Class structured model (Caswell, 1989, pp. 83–93), the matrix projection model from Figure 3 is parameterised as such: $α_{i} = p_{i} (1 - g_{i})$ , $γ_{i} = p_{i} g_{i}$ , and $β_{i} = p_{1}^{0.5} \frac{1}{2} ((1 + α_{i}) m_{i} + γ_{i} m_{i + 1})$ . For this example, consider that collectives cannot shrink by setting $μ_{i} = 0$ .

In this model, the optimal trait value for counterfactual ( $f_{2}$ ) fitness is always a null investment in collective survival $θ = 0$ . However, the optimal trait value for whole life cycle fitness ( $F$ ) is $θ > 0$ . Thus, if a population starts with the optimal trait value for the counterfactual fitness $θ_{0} = 0$ , it will evolve towards the optimal value $θ^{*} > 0$ (Figure 5; green arrow). Over time, collective-level fitness $F$ increases while counterfactual fitness $f_{2}$ decreases.

Figure 5

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The tradeoff model can reproduce the fitness-decoupling observation.

(a) Values of $F$ andf2 as a function of the trait $θ$ . (b) Ancestral and derived values of whole life cycle fitness ( $F$ ). (c) Ancestral and derived values of counterfactual fitness ( $f_{2}$ ). The expected evolutionary trajectory from ancestral (θ₀) to derived (θ^*) trait value (green arrow in (a)) results in an increase of $F$ and a decrease of , reproducing the fitness-decoupling observation of Figure 1. Parameters: $N = 30$ , $η = 8$ , and $p_{1} = 0.1$ .

This evolution towards higher values of $θ$ (because it increases $F$ ) coinciding with a decrease in $f_{2}$ leads to a fitness-decoupling observation. Note, importantly, that following the assumptions of the model, the opposite directions of the dynamics of $F$ and $f_{2}$ are a consequence of optimal trait values constrained by a tradeoff being different in different environments, rather than an inherent relationship between them. To see this, consider the example of selection for fast settlement in Saccharomyces cerevisiae (Ratcliff et al., 2012). The optimal trait value for an ancestral particle (i.e., a free living cell) is having round cells. However, in a snowflake aggregate, the optimal shape is to be elongated because this shape permits packing of more cells. In this example, $f_{2}$ decreases—to be elongated in the ancestral environment would be disadvantageous—when whole life cycle fitness $F$ increases: to be elongated is advantageous in the context of the snowflake. Suppose for an instant that elongated cells were also favoured in the unicellular context, but the initial conditions of the dynamics were still round cells: the evolutionary trajectory in a collective context would not be modified. The value of the counterfactual fitness, in and of itself, has no consequence for the outcome of selection in the collective context: it is not because $f_{2}$ decreases (and is transferred to $F$ , or is decoupled from $F$ ) that the transition occurs. The trait values evolve according to $F$ . There is no direct causal relationship between $f_{2}$ and the observed changes in traits. Relative changes in $F$ and $f_{2}$ do not cause the dynamics observed but rather follow from changes in environmental conditions and genetic and phenotypic constraints on cells. Nevertheless, we consider the counterfactual fitness approach (Shelton and Michod, 2014) a valuable tool to detect tradeoffs between traits in the context of ETIs. This approach can also be used to generate hypotheses about the traits of the unicellular ancestor by considering that ancestral traits had an optimal value for counterfactual fitness.

In the next section, we propose to go one step further and evaluate how the capacity for a lineage to break away from such a tradeoff could be used to detect an ETI. Patterns of tradeoff breaking correspond with the emergence of novel collective-level traits—that is, traits that can only be exhibited in a collective context—and, as such, provide an evolutionary cause of ETIs.

4. Tradeoff breaking as a marker of an ETI

In the previous section, we saw that a tradeoff between traits can result, under specific conditions, in an empirical fitness-decoupling observation. Evolutionary tradeoffs between traits are a consequence of the genetic background of organisms and their environment. Thus, they are not immutable and can evolve if some changes in the genetic background or the environment occur. In this section, we propose that a marker of an ETI is ‘breaking’ from the initial tradeoff (hereafter called ‘tradeoff-breaking’ observations). To explain this phenomenon, we present a modification to the model described in Section 3, which we call the ‘tradeoff-breaking model’.

A tradeoff is essentially a constraint on the combined values of a set of traits; it prevents a given organism from simultaneously performing well in two or more functions—for instance, growth and survival or photosynthesis and nitrogenase activity in cyanobacteria, as discussed below. Thus, if a mutant lineage is able to bypass the tradeoff and perform well in different functions, it is expected to be fitter than its ancestor and increase in proportion in the population. In some cases, mutations that lead to a multicellular morphology might be a necessary step towards bypassing or breaking the tradeoff. This provides an ‘adaptive’ explanation for the emergence of multicellular organisms. Collectives (i.e., multicells) emerge by mutations constrained by the tradeoff, but their long-term persistence is rendered more probable by tradeoff-breaking mutations that would not have been possible, or would not have broken the tradeoff, had they occurred in their unicellular ancestors.

To illustrate this point, we provide two examples from biology. The first is the well-understood tradeoff between photosynthesis and nitrogen fixation—from dinitrogen gas (N₂)—in cyanobacteria. The tradeoff is caused by the oxygen sensitivity of the enzyme nitrogenase, which catalyses the process of reducing N₂ to ammonia (NH₃). This prevents cells from performing both functions simultaneously and has resulted in several morphological and physiological adaptations (Figure 6a). In the unicellular species, Cyanothece sp. ATCC 51142 and Crocosphaera watsonii WH8501, and the undifferentiated filamentous Plectonema boryanum UTEX 594, the two functions are separated temporally by a circadian rhythm: the oxygen-sensitive N₂ fixation is performed during the night, unhindered by the oxygen-producing photosynthesis during the day. When plotting the activity values for photosynthesis and N₂ fixation for populations of these species, they fall on both sides of the tradeoff—depending on the time of the day (Figure 6b). In the morphologically undifferentiated filamentous multicellular Trichodesmium sp. IMS101, the two functions are performed simultaneously but in different, morphologically identical cells of the filament. Thus, the values for these populations are located in the middle of the tradeoff—they perform averagely in both functions. This pattern can also be seen for populations of the highly differentiated filamentous Anabaena oscillarioides, which perform even better than the undifferentiated Trichodesmium sp. This can be explained by the presence of differentiated cells (heterocysts) that only fix N₂ and exchange the fixed nitrogen compounds against carbon products with the photosynthesising cells of the filament. This example seems to be compatible with the tradeoff-breaking framework—both multicellular and (physiologically) differentiated species, (a) Anabaena oscillarioides and Trichodesmium sp., seem to have broken away from the tradeoff, which leads to tradeoff-breaking observations in Figure 6b (indicated by asterisks). Moreover, photosynthesis and nitrogen fixation are positively associated, as indicated by the regression line. Overall, the example of cyanobacteria illustrates how tradeoff breaking can occur—multicellular differentiated morphology and designated N₂-fixing cells allow the organisms to break away from the tradeoff that is present in the unicellular and physiologically undifferentiated phyla (visible in Figure 6b as the three negative regression lines).

Figure 6

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Tradeoff-breaking lineages can be inferred experimentally.

(a) Morphological and physiological N₂-fixing adaptations for different cyanobacteria. Orange shaded areas indicate nitrogenase localisation. Daily rhythm of photosynthesis (solid line) and N₂-fixation (dashed line) (modified from Figure 2 of Berman-Frank et al., 2003). (b) Tradeoff between photosynthesis activity and nitrogenase activity in cyanobacteria (data taken from Colón-López et al., 1997; Mohr et al., 2013; Misra and Tuli, 2000; Berman-Frank et al., 2001; Popa et al., 2007 and standardised). The shaded area for a given species corresponds to the convex hull of observations. Assuming a representative sampling, it stands for the expected range of traits accessible for this species. Dashed lines are least-square linear regressions of the observations of each species; asterisks indicate potential tradeoff-breaking observations because they depart notably from the tradeoff pattern displayed by most species. (c) Tradeoff between collective persistence and cell number in *Pseudomonas fluorescens* for ancestral and derived lineages (Hammerschmidt et al., 2014; asterisks indicate tradeoff-breaking observations in two lineages). Dataset published as Rose et al., 2018.

The second example is the derived P. fluorescens populations, where tradeoff breaking seems to have occurred in some of the evolved lineages. In this case, the tradeoff implies that collective persistence cannot increase concomitantly with cell number. However, in the experiment of Hammerschmidt et al., 2014, two lineages have succeeded in doing this, leading to two tradeoff-breaking observations visible in Figure 6c (indicated by asterisks). Here, collective persistence increased due to the evolution of a mutS-dependent genetic switch that enabled rapid and predictable transitioning between two stages of a life cycle. This increase in collective persistence is not accompanied by a decrease in cell density, as is the case in other lineages, indicative of these two lineages having broken the tradeoff.

The model presented in Section 3 cannot account for such changes affecting the traits, for example, through mutations. To do so, it must be modified into what we refer to as the tradeoff-breaking model. In the model presented in Section 3, the traits survival $s$ and growth $b$ were linked by a deterministic relation through the investment trait $p$ : $s = p$ and $b = 1 - p$ . Thus, any mutation affecting one trait necessarily leads to opposite effects on the other trait. This assumption can be relaxed, allowing the two traits to take any pair of values. To keep modelling the tradeoff, we suppose that the distribution of mutational effects (the mutation kernel) is a two-dimensional Gaussian distribution with a high (negative) correlation value $(ρ = - 0.9)$ . This means that most mutations that increase one trait value reduce the other. However, and this is crucial, some rare mutations have the effect of increasing or decreasing both values, something that was impossible in the model described in Section 3. Thus, Eq. 2 becomes

\frac{d}{d t} (\begin{matrix} s \\ b \end{matrix}) = F (s, b)^{- 1} (\begin{matrix} σ_{s}^{2} & σ_{s} σ_{b} ρ \\ σ_{s} σ_{b} ρ & σ_{b}^{2} \end{matrix}) \nabla F (s, b)

where $F (s, b)$ is the whole life cycle fitness as a function of the traits, $\nabla F (s, b)$ is the fitness gradient in the two-dimensional trait space, and $σ_{s}$ and $σ_{b}$ are the variance of mutational effects on $s$ and $b$ , respectively. Figure 7 shows the trajectory resulting from this model. Initially, the population moves along the tradeoff in the trait space: reducing the value of $b$ and increasing the value of $s$ . This reflects how ‘low-hanging fruit’ mutations—mutations that are more frequent due to the skew in the mutational effect distribution—drive the initial dynamics. This fast-paced phase of the dynamics (which can be absent in some cases; see next section), following a phase during which collectives are formed, ends when the population reaches the neighbourhood of the optimal organism that lies on the tradeoff line $s = (1 - b)$ (around $t_{1}$ ). Then, a slower phase of the dynamics starts and leads to a tradeoff-breaking observation (the population ‘breaks away’ from the tradeoff line; Figure 7a after $t_{1}$ ). This third phase is slower because mutations that move collectives in this direction are statistically less likely to occur. Figure 7b shows that observation of fitness decoupling between $f_{2}$ and $F$ could only be made in the first part of the trajectory. However, the whole trajectory is characterised by an increase in fitness $F$ , as discussed in Section 3.

Figure 7

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Tradeoff-breaking mutations do not fit the fitness-decoupling observation.

(a) Trait space with isolines of fitness. An example of a possible evolutionary trajectory is shown in green. (b) Particle (counterfactual; $f_{2}$ in red) and collective fitness ( in orange) values along the example evolutionary trajectory (in green). The strict tradeoff from Section 3 and Figure 5 is shown in purple. The times marked by vertical lines in (b) correspond to the dots in (a). The evolutionary trajectory can be separated into two phases once collectives have been formed: a fast-paced phase (before $t_{2}$ ) that closely follows the purple tradeoff in (a) and a slower phase (after $t_{1}$ ) that breaks away from it and leads to the tradeoff-breaking observation. Note that a fitness-decoupling observation can only be made in the fast-paced phase of the trajectory (before $t_{2}$ ), as represented in (b). Parameters: $N = 15$ , $p_{1} = 0.1$ , $η = 8$ , $ρ = - 0.9$ .

Our model gives a simple mechanism that can reproduce the experimental fitness-decoupling observation, in addition to the tradeoff-breaking observations due to rare mutants. Specifically, we observe that the trajectory resulting from the model is mirrored by the trajectory of lineages in the evolved P. fluorescens populations (Hammerschmidt et al., 2014). When compared to the ancestral lineages, most of the evolved lineages appear to have been constrained by the tradeoff and increased in collective persistence at the expense of cell density (through low-hanging fruit mutations, as is the case between $t_{0}$ and $t_{1}$ in Figure 7). Notably, only the two outlier lineages (marked by asterisks in Figure 6c) seem to have started to break away from the tradeoff—they seem to have reached the slower phase of the evolutionary dynamic (where less likely mutations are explored, as is the case between $t_{1}$ and $t_{2}$ in Figure 7). Tentatively, the fact that only the two outlier lineages broke away from the tradeoff might be due to a higher mutation rate increasing the relative speed of evolution compared to the other lines. According to our tradeoff-breaking framework, the fitness-decoupling observation should be reinterpreted as lineages being in the fast-paced phase of the trajectory. Moreover, the tradeoff-breaking lineages should be explored (as done to an extent in Hammerschmidt et al., 2014) as we advocate that such tradeoff-breaking observations in this context are the mark of significant innovation and, thus, can be used to detect ETIs.

The tradeoff-breaking model presented here is compatible with a number of different models of ETIs recently proposed in the literature. Among them are two models we think could benefit from being seen through the framework we have developed here because they illustrate a diversity of mechanisms that yield initial tradeoffs and tradeoff-breaking mutations: the ratcheting model proposed by Libby and collaborators (Libby et al., 2016; Libby and Ratcliff, 2014) and the ecological scaffolding model proposed by Black et al., 2020. Further, recasting these two models in terms of tradeoff breaking yields new insights, which are detailed in Box 2 and Box 3, respectively.

Box 2

Ecological scaffolding and tradeoff breaking.

Population structure can lead to the kind of tradeoff presented in Section 3, as seen in the ecological scaffolding scenario for the origin of multicellularity (Black et al., 2020). In this scenario, the population of particles is structured in patches of finite resources with dispersal between patches. The tradeoff in this model is between trait values that enhance particle performance within patches and trait values that favour dispersal to new patches. The evolutionary dynamics of two particular traits are studied: particle growth rate and production of soma-like particles that do not disperse themselves but favour the dispersal of the other particles in the patch. In this box, we show how the model of Black et al., 2020 captures the concepts of tradeoff and tradeoff breaking presented in the main text.

Ecology

We model the dynamics of germ cells ( $g$ ), soma cells ( $s$ ), and resources ( $r$ ) within collectives. Two traits can mutate: the growth rate of germ cells $β$ and the proportion of soma cells that are produced by germ cells $q$ . The ecology within a patch is given by (Equation 3 in Black et al., 2020)

{\begin{cases} \frac{d g}{d t} = & N^{- 1} β (1 - q) r (t) g (t) - g (t) \\ \frac{d r}{d t} = & - N^{- 1} β r (t) g (t) - d r (t) s (t) \\ \frac{d s}{d t} = & N^{- 1} β q r (t) g (t) - s (t) \end{cases},

where $N$ is the carrying capacity of a patch and $d$ the rate at which soma cells consume resources. Initial conditions at the beginning of each generation are taken to be $g (0) = 1$ , $r (0) = N$ , and $s (0) = 0$ . Thus, at the beginning of a collective generation, there is only a single germ cell in the collective. Note that if $q = 0$ , there are never any soma cells in the model (for any point $t$ , $s (t) = 0$ ).

The weight of a patch $w$ in the dispersal phase is given by $w = (1 + ρ s (T)) g (T)$ , where $T$ is the duration of the growth phase and $ρ$ is the advantage in dispersal conferred by the soma cells. If $ρ = 0$ , the soma cells do not affect the dispersal.

Fitnesses

We now recast this model within our framework. The within-collective fitness of cells $f_{1}$ (ignoring inter-collective events and density dependence within collectives) is $f_{1} = {\frac{d (s (t) + g (t))}{d t} |}_{s, r, g = (1, N, 0)} = β$ . The counterfactual fitness $f_{2}$ is computed, assuming that collectives give rise to free living cells at rate $β$ (and not allowing the production of soma cells); thus, $f_{2} = β$ .

Computing the whole life cycle fitness $F$ (or $f_{3}$ ) is more challenging since there is (some) density dependence between collectives. However, since collective generations are non-overlapping and collectives only reproduce once (at the end of their life), the only number that matters, in the long run, is the weight of a patch (the number of dispersing propagules) at the time of dispersal: $F \approx w$ .

Box 2—figure 1a shows the set of accessible phenotypes when mutations occur on either $β$ or $q$ . From this figure, it is possible to predict what will happen in a hypothetical scenario of sequential mutations on $β$ then $q$ . Starting from point a, if only $β$ is able to mutate, we can expect the population to move to b (the highest value of $F$ for $q = 0$ , while $f_{2}$ decreases), optimising on the tradeoff. Note that $β$ plays the same role as $θ$ in Section 3, encoding the linear abscissa of the cells on the tradeoff line. If mutations affecting $q$ become possible once the population reaches $b$ , the population is expected to evolve towards $c$ , without change in $f_{2}$ , breaking the previously defined tradeoff. This requires that mutations happen on one trait and then the other. This assumption will be relaxed in the next paragraph by using the same method as in Section 4.

Evolution

Let $(q, β)$ be the vector of traits characterising a phenotype. We compute the evolutionary trajectory using the same Lande equation model as in Section 4: namely, Eq 3. $G$ is the variance–covariance matrix of mutational effects. In this example, consider that mutational effects on both traits are not correlated ( $ρ = 0$ , using the notation of the main text), and that the mutational effect variance for $β$ is much higher than for $q$ : $σ_{β} = 0.1$ and $σ_{q} = 0.001$ . This assumes that most mutations have a higher effect on $β$ than $q$ .

Box 2—figures 1b and c show a trajectory simulated this way, with initial conditions $(q_{0}, β_{0}) = (0, 1.8)$ , which displays a dynamic akin to the one in Section 4: a fast-paced phase where frequent low-hanging fruit mutations (mainly affecting $β$ ) are reached by the population, increasing $F$ (between $t_{0}$ and $t_{1}$ , note that $f_{2}$ simultaneously decreases). This fast-paced phase is followed by a slow-paced phase where an increase in $F$ is only possible through rarer mutations (mainly affecting $q$ ) (after $t_{1}$ ; note that $f_{2}$ simultaneously increases) and leads to a tradeoff-breaking observation similar to the one described in Section 4.

To summarise, this simple set of hypotheses (initial conditions, rarer mutations on $q$ than on $β$ ) leads to a transient fitness-decoupling observation. Notably, this observation does not stem from mutational effects (like in the main text), but from the ecological constraints on $β$ that do not allow $F$ and $f_{2}$ to be maximised for the same conditions (purple line in Box 2—figure 1a). Tradeoff breaking is due to rarer mutations on $q$ (as in the main text where rare mutations increase both survival and growth rate).

Box 2—figure 1

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Tradeoff breaking in the ecological scaffolding scenario.

(a) Values of $F$ and $f_{2}$ accessible to the organism when $q = 0$ and only $β$ can mutate (purple) and values of $F$ and $f_{2}$ accessible to the organism when only $q$ can mutate and $β$ is such that $F$ is maximum for $q = 0$ (black); (b) trait space with isolines of fitness ( $f_{2}$ in red, $F$ in orange), with an example of evolutionary trajectory in green (ancestral tradeoff represented in purple). (c) $f_{2}$ and $F$ values along the example evolutionary trajectory. The times marked by vertical lines in (c) correspond to the dots in (b). Note that $F$ and $f_{2}$ have opposed dynamics from $t_{0}$ to $t_{1}$ (fitness-decoupling observation) and both increase from $t_{1}$ to $t_{2}$ . Rare mutations on q allow breaking away from the ancestral tradeoff line (tradeoff-breaking observation). Parameters: $N = 1 e + 06$ ; $T = 30$ ; $d = 0$ ; $ρ = 0.01$ ; $σ_{β} = 0.1$ ; $σ_{q} = 0.001$ .

Box 3

Ratcheting and tradeoff breaking.

Tradeoff-breaking mutations are equivalent to rare mutations that change the set of accessible phenotypes. Libby et al., 2016 propose a mechanism of ratcheting mutations that stabilises multicellularity by constraining evolutionary reversion towards unicellularity. They consider a nascent multicellular organism that switches between a multicellular $G$ and unicellular state $I$ , growing in an environment alternating between two states, one favouring the multicellular life cycle ( $E_{G}$ ) and the other favouring the unicellular life cycle ( $E_{I}$ ). Two types of ratcheting can occur: first, mutations that improve the fitness within the multicellular type that come at a cost to the free-living type (reducing the fitness of revertants) and, second, a type of ratcheting mutation that decreases the probability that a mutation results in reversion. In the following, we show how the slowest of type 1 or type 2 ratcheting fits as a tradeoff-breaking mechanism, as presented in the main text.

The population dynamics of both types $G_{t}$ and $I_{t}$ in an environment that fluctuates between $E_{G}$ and $E_{I}$ after a fixed number of generations in each ( $n_{g}$ and $n_{i}$ , respectively) is given by Equation 2.3 from Libby et al., 2016

\begin{array}{ll} (\begin{matrix} G_{t + n g + n i} \\ I_{t n g + n i} \end{matrix}) & = {(\begin{matrix} (1 - c i) (1 - p) + 1 & p \\ (1 - c i) p & 1 + (1 - p) \end{matrix})}^{n_{i}} {(\begin{matrix} 1 + (1 - p) & (1 - c_{g}) p \\ p & (1 - c_{g}) (1 - p) + 1 \end{matrix})}^{n_{s}} (\begin{matrix} G_{t} \\ I_{t} \end{matrix}) \\ = A_{I}^{n i} A_{G}^{n g} (\begin{matrix} G_{t} \\ I_{t} \end{matrix}) = A (\begin{matrix} G_{t} \\ I_{t} \end{matrix}), \end{array}

where $p$ is the probability for cells to switch from one type to the other, and $c_{g}, c_{i} > 0$ are the fitness differences between $G$ and $I$ cells in $E_{G}$ and $E_{I}$ environmental states, respectively. In the following, we fix $c_{g} = 0.1$ , and the traits that can mutate are $p$ and the fitness gap $Δ c = c_{g} - c_{i}$ .

We now recast this model within our framework. The whole life cycle fitness of the organism $F$ is the log of the dominant eigenvalue of the matrix $A$ ; the counterfactual fitness $f_{2}$ is the fitness of the organisms if they would always be in the $E_{I}$ environment ( $n_{g} = 0$ )—that is, the log of the dominant eigenvalue of $A_{I}$ . Conversely, the within-collective fitness $f_{1}$ is the fitness of the cells if they would constantly be in the $E_{G}$ environment—thus, the log of the dominant eigenvalue of $A_{G}$ .

Let $(Δ c, p)$ be the trait vector characterising a phenotype, and let us model evolution using the equation from Section 4, Equation 3, considering that mutations affecting $p$ (ratcheting type 2) are more frequent than mutations affecting $Δ c$ (ratcheting type 1): $σ_{Δ c} = 10^{- 4}, σ_{p} = 0.2$ . Initial trait values are $Δ c = 0$ and $p = 10^{- 5}$ (no fitness gap and very rare switch).

Box 3—figures 1b and c show the result of the simulation. The evolutionary trajectory can be split into three phases: first, a fast-paced phase where the switch probability p increases to 0.2, corresponding to optimisation on the tradeoff (before $t_{1}$ , note that here p plays the same role as $θ$ in Section 3, giving the linear abscissa of the cells on the tradeoff line); then a slow increase in $Δ c$ , corresponding to the slow accumulation of tradeoff-breaking mutations (type 1 ratcheting) leading to a tradeoff-breaking observation (between $t_{1}$ and $t_{2}$ ); and, finally, a new decrease in switch probability (type 2 ratcheting), corresponding to an optimisation on the (new) tradeoff (after $t_{2}$ ). The result is an overall increase in the proportion of G-type in the population (Box 3—figure 1c). Note that $F$ always increases along the trajectory. However, $f_{2}$ decreases in the first phase and increases in the second and third phases, showing trajectories for which the fitness-decoupling model cannot easily account.

To summarise, this simple set of hypotheses (ratcheting types 1 and 2, with mutations for ratcheting 1 being rarer) leads to a fitness-decoupling observation when selection first acts along the switch probability tradeoff (leading to higher switching and an increase in multicellular types) because the optimal trait values for $F$ and $f_{2}$ are different. Then, rarer type 2 ratcheting mutations result in tradeoff breaking, eventually resulting in a second (relatively fast-paced) optimisation on the switch-probability tradeoff (leading to reduced switching and entrenchment of the multicellular type), which does not result in a fitness-decoupling observation because the optimal trait values for $F$ and $f_{2}$ coincide. Note that, here, the tradeoff stems from the ratcheting mechanism and the environment periodically switching between multicellularity or unicell-favouring, rather than the genetic architecture (as in the main text) or population structure (as in Box 2).

Box 3—figure 1

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Ratcheting and tradeoff breaking.

(a) Values of $F$ and $f_{2}$ accessible to organisms when $Δ c = 0$ and $p$ is free (purple), and when $p = 0.2$ and $Δ c$ is free (black). (b) Trait space with isolines of fitness ( $f_{2}$ in red, $F$ in orange) with an example of evolutionary trajectory in green (ancestral tradeoff represented in purple). (c) Fitness values for $f_{1}$ (in brown), $f_{2}$ , and $F$ , in addition to the stable proportion of G (in blue) along the example evolutionary trajectory. The times marked by vertical lines in (c) correspond to the dots in (b). Note that $F$ and $f_{2}$ have opposed dynamics from $t_{0}$ to $t_{1}$ (fitness-decoupling observation), and both increase after $t_{1}$ . Rare mutations on $Δ c$ allow breaking away from the ancestral tradeoff line (tradeoff-breaking observation) after $t_{1}$ . Parameters: $c_{g} = 0.1$ ; $σ_{Δ c} = 10^{- 4}, σ_{p} = 0.2$ .

In the ratcheting model, proto-multicellular organisms are in an environment alternating between multicell-favouring and unicell-favouring. This yields a tradeoff between the two states and the selection for a high probability of multicells to revert to unicells. Some mutations (‘ratcheting (type 1) mutations’) are assumed to be beneficial in a collective (multicellular) environment while deleterious in a unicellular context; thus, they play the tradeoff-breaking role. Libby et al., 2016 showed, through simulations, that the accumulation of ratcheting mutations makes it harder for a multicellular organism to revert to a unicellular state even when the environment becomes favourable for unicellularity.

In the ecological scaffolding model, the environment, structured both spatially and temporally, allows for selection of collective-level properties without the need to assume anything about the particles other than that they reproduce at different rates. Black et al., 2020 showed that the tradeoff stems from population structure: reductions in cell growth rate are favoured due to benefits to collectives that are realised via improvements in dispersal. The emergence of specialised soma cells is an example of tradeoff breaking: it allows an increase in collective dispersal without requiring as much cell growth reduction.

Both models illustrate the flexibility of our tradeoff and tradeoff-breaking approach. First, it allows multiple mechanisms of evolutionary transitions to be formalised in a unified way. Second, tradeoff-breaking observations can be used as a general marker across various mechanisms of evolutionary transitions.

5. The trait-based approach in the context of ETIs

The trait-based approach we have described so far delineates an adaptive scenario for an ETI. This scenario is divided into several phases. These are, first, the formation of collectives, in which individuation mechanisms that might be adaptive are at play (Clarke, 2013; Clarke, 2014); second, an optimisation within the constraints of the ancestral tradeoff (note that this phase is optional and might be shortened or bypassed depending on the biological system); and third, a tradeoff-breaking phase. In this section, we recast this scenario in the broader context of ETIs and discuss its relevance as a marker of individuality.

Before an ETI starts, the unicellular ancestors have been selected for traits that optimise growth rate in a unicellular environment under the constraints of their genetic constitution (‘Tradeoff-optimal particle phenotype’; blue disk in Figure 8). Then, a mutation (e.g., loss of the transcription factor ACE2, resulting in snowflake-shaped yeast clusters; see Ratcliff et al., 2015), a plastic change in phenotype (e.g., filament formation under low population densities in cyanobacteria; see Tang et al., 2022), a change in the structure of the environment (as in the ecological scaffolding model for the origin of multicellularity; see Black et al., 2020), or even a combination of several factors (‘wrinkly spreader’ mats arising by mutation and ecological scaffolding; see Hammerschmidt et al., 2014) promote the formation of collectives (Figure 8). Multicellular collectives define a new environment where the optimal trait values are potentially different. We assume here that this change is abrupt and not accompanied by the immediate disappearance of the underlying constraints that bear upon the cell traits, particularly tradeoffs, due to the rest of their genetic machinery. Collective formation is the first phase of our scenario and is often the first phase of any descriptions of an ETI (Bourke, 2011; (c) Rose and Hammerschmidt, 2021; van Gestel and Tarnita, 2017). This has been studied in detail by Tarnita et al., 2013, particularly in the context of competition with the unicellular ancestor. In contrast, our model focuses on what happens after the initial formation of collectives.

Figure 8

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An adaptive scenario for evolutionary transitions in individuality as a consequence of the trait-based approach.

(1) Collective formation of particles occurs through an event that does not change the focal traits. (2) Optimisation ‘on the tradeoff’, where the traits are selected within the constraints passed down from the ancestral organism. (3) Tradeoff breaking, where mutations that are not bound by the ancestral constraints enable tradeoff breaking. Fitness-decoupling observations are expected in the second phase but not in the third. Note that the second phase might be shortened or even bypassed depending on the mutational path (this second route ‘immediate tradeoff breaking’ contrasts with the previously described first route ‘fast-slow dynamics’). This framework can be used to interpret a diversity of experimental and mathematical model systems as shown with the examples: *P. fluorescens* from Hammerschmidt et al., 2014, *S. cerevisiae* from Ratcliff et al., 2015, ecological scaffolding from Black et al., 2020, and ratchet model from Libby et al., 2016.

In a second phase, we expect changes in traits to occur due to low-hanging fruit mutations, which remain constrained by the ancestral tradeoffs. We call this phase ‘optimisation on the tradeoff’, and it leads the system towards an optimal phenotype for the within-collective environment (‘Tradeoff-optimal collective phenotype’; orange disk in Figure 8). We observe trait optimisation on the tradeoff in all our example model systems (Figure 8), except for cyanobacteria. Here, in contrast to the other empirical examples, we do not follow an ETI in progress but one that happened in the evolutionary past so that phase 2 cannot be observed (anymore) in the known multicellular species of today. During this phase in our scenario, fitness decoupling might be observed. For this to occur, the system must meet a few assumptions we made in the previous section: namely, that fitness is a continuous function of traits, and that the ancestral traits are initially optimal for the single-cell environment—and, thus, optimal for counterfactual fitness—but not optimal for the within-collective environment. When these assumptions are met and selection drives the system towards better trait values (within constraints) for this new within-collective environment, counterfactual fitness will necessarily decrease while collective fitness will necessarily increase (from the blue to the orange disk in Figure 8). If this set of assumptions is violated, nothing can be said about the relationship between counterfactual and collective fitness.

The third phase entails changes in phenotype that lie outside the constraints of the ancestral particles. These are driven by selection of the system towards new, previously unreachable trait values (‘unconstrained optimal collective’; red disk in Figure 8). We refer to this third phase as the tradeoff-breaking phase (see Figure 8 for adaptations in our example model systems). During this phase, particle fitness—whether counterfactual ( $f_{2}$ ) or within collectives ( $f_{1}$ )—does not necessarily continue to decrease, even if the conditions for fitness-decoupling observations outlined earlier are fulfilled. This is so because the new trait values are in the region of the trait space that was not reachable by the ancestor. In consequence, there is no particular theoretical or biological reason to expect that they would have been suboptimal and selected against, had the ancestor been endowed with such trait values.

If we assume that tradeoff-breaking changes are less likely than the low-hanging fruit mutations constrained by a tradeoff, we statistically expect them to occur predominantly after the second phase, resulting in a ‘fast-slow dynamic’ (route 1 in Figure 8). This route is the focus of this article. However, while we do not develop this in detail here, depending on the biological system, the second phase might be short if tradeoff-breaking changes are the first to occur. This possibility is particularly relevant for experimental studies. A short second phase implies that it could easily be missed by experimenters. Another possibility is that the second phase is missing entirely (route 2 in Figure 8).

Yet another possibility not studied in this article is that tradeoff-breaking-like observations could be made immediately after or even during the formation of a collective, leading to the spontaneous emergence of properties that also confer the collective living benefits. Thus, tradeoff-breaking dynamics (whether following route 1 or route 2 in Figure 8) could be driven entirely by the phenotypic plasticity of particles, without the need for mutation. For instance, in clonal collectives, one could imagine that phenotypic heterogeneity leads to a primordial form of division of labour (Ispolatov et al., 2012; Ulrich et al., 2018; van Gestel and Tarnita, 2017 for details), which would provide such collectives with an immediate selective advantage (Ispolatov et al., 2012; Ulrich et al., 2018). In this ‘plasticity first’ scenario, the different phenotypic states would already be part of the genetic repertoire of the unicellular ancestor.

Our main objective in advocating this trait-based approach is to offer a consistent framework for interpreting models, empirical observation, and evolutionary experiments of ETIs, which can accommodate the apparent fitness-decoupling observations, in addition to the tradeoff-breaking ones, without referring to the export-of-fitness metaphor. Provided this empirical objective, it is legitimate to ask to what extent the tradeoff-breaking scenario is representative of ETIs and can be used as a marker that an ETI is underway or has occurred. First, one must recognise that tradeoff breaking might occur outside ETIs. For instance, tradeoff breaking and, more generally, ‘constraints breaking’ are already considered key events in the evolution of body plans and are expected to be a widespread mechanism for the emergence of novelties (see Galis and Metz, 2007; de Vos et al., 2015). Thus, a tradeoff-breaking event in and of itself cannot be used as a marker of an ETI. However, considering a trait in the context of an ETI, where collectives are formed and maintained (phases 1 and 2), and establishing how those collectives change and potentially overcome the constraints that historically bear on particles (phase 3) offers a good empirical handle to study ETIs. Conversely, the lack of any tradeoff-breaking observation in such an empirical system could be used as an indication that the transition is still in its early stages.

Discussion

Fitness-centred approaches to ETIs have been influenced by the concept of fitness-decoupling between lower-level particles and higher-level collectives. In this view, the fitnesses of particles and collectives are initially proportional to one another but diverge as an ETI occurs—particle fitness decreases while collective fitness increases. This interpretation comes with some inconveniences. First, fitness is notoriously difficult to define and measure. This, in turn, makes fitness comparisons across levels difficult. Second, fitness values in and of themselves do not provide a mechanistic model of the system. Progress in understanding ETIs relies on our ability to circumvent limitations inherent in the currency of fitness. We suggest that, to study ETIs, focusing on traits and tradeoffs between traits, rather than focusing on fitness, is both more parsimonious and practically achievable. Finally, we propose that rare tradeoff-breaking events are a crucial part of ETIs and could be used experimentally for their detection.

Our first main finding is a new formal argument cementing the position that decoupling between commensurable measures of fitness is impossible. Starting from the recognition that fitness is a concept difficult to define consistently (Abrams, 2012; Ariew and Lewontin, 2004; Doulcier et al., 2021), the problem is magnified when the entities to be compared belong to different levels of organisation. As we discuss in Section 1 (and Box 1), experimentally comparing fitness in such cases would require being able to measure the growth rates in the same environment at different levels of organisation, which proves challenging. Even if such a comparison could be made, fitness measures at different levels of the same biological substrate necessarily lead to the same outcome at any level. We show this point formally in Section 2. In particular, commensurability is assured by taking care to use the same set of events (same reference environment and same timescales) for both measures. Once this is ensured, fitness decoupling is not observed. Thus, our analysis reveals that fitness-decoupling observations result from incommensurable fitness measurements. We formally confirm the analysis provided by Bourrat, 2015a; Bourrat, 2015b (see also Black et al., 2020), who qualify such observations as artefacts of descriptions and confirm the result of Shelton and Michod, 2014 that ‘cells and colony level fitness […] are mathematically equivalent ways of bookkeeping’ (p. 457) by extending it to more general models of population dynamics. Counterfactual particle fitness does not suffer from this problem and can vary independently of actual fitness. Thus, it can be used to characterise evolutionary tradeoffs in the context of ETIs. However, we highlight the fact that this counterfactual value is not compatible with the fitness transfer metaphor because it is a theoretical construct and not an actual quantity to be transferred (but see Shelton and Michod, 2020, for a diverging opinion on the subject).

Our second main result is a general adaptive scenario of ETIs that is compatible with both experimental fitness-decoupling observations (artifactual or counterfactual) and tradeoff-breaking deviations. In Section 3, we clarify the conditions under which a fitness-decoupling observation (between incommensurable fitness measures) could, in principle, be made—using a simple tradeoff model between trait values, we find that one condition is that the optimal trait values for counterfactual particle fitness and whole life cycle fitness are different. In Sections 4 and 5, we show that if the tradeoff is relaxed through the existence of rare tradeoff-breaking events, fitness-decoupling observations may not hold for whole evolutionary trajectories. We suggest that an evolutionary trajectory can be divided into three phases: a first phase during which collectives are formed, followed by an optional second fast-paced phase during which optimisation ‘on the tradeoff’ occurs, and, finally, a slower phase driven by rare tradeoff breakings. Tradeoff-breaking mutations might result in lineages where both counterfactual and whole life cycle fitnesses are increased compared to the ancestor. We propose that departures in collective-level entities from ancestral tradeoffs—tradeoff-breaking points—are a mark of a key moment in ETIs and might be used to characterise them. This proposal is compatible with recent models found in the literature on ETIs—namely, the ecological scaffolding model (Black et al., 2020; Bourrat, 2022; Doulcier et al., 2020) and the ratchet model (Libby et al., 2016; Libby and Ratcliff, 2014)—that provide alternative mechanisms for both tradeoffs and tradeoff-breaking observations. Further, we show that it is also compatible with experimental data on cyanobacteria (Colón-López et al., 1997; Misra and Tuli, 2000; Berman-Frank et al., 2001; Berman-Frank et al., 2003; Popa et al., 2007; Mohr et al., 2013) and P. fluorescens (Hammerschmidt et al., 2014; Rose et al., 2020).

Our tradeoff-breaking framework could also serve as a springboard to generate new hypotheses. The study of tradeoff breaking requires estimating changes between the pre-ETI ancestral traits (e.g., unicellular) and post-ETI derived traits. Access to ancestral traits can be gained in multiple ways, depending on the system studied. The first is through phylogenetic reasoning, such as by reconstructing the sequence of ecological and phenotypic trait evolution during the evolution of cyanobacterial multicellularity (as in Hammerschmidt et al., 2021). The second is by assuming that the ancestral traits are close to the optimal values with respect to the counterfactual particle ‘outside of the collective’. The counterfactual method described by Shelton and Michod, 2014 is useful here. The third is through direct measurement during experimental evolution studies (Ratcliff et al., 2012; Hammerschmidt et al., 2014; Herron et al., 2019). Additionally, statistical methods to better characterise tradeoff breaking should be developed.

Fitness-centred approaches to ETIs may have reached their limits. We propose to refocus the problem on tradeoffs between traits, thereby bypassing the difficulties inherent to fitness comparisons. The advantages of this move are multiple and range from allowing better experimental accessibility to producing a more mechanistic theory. The way the collective-level context affects the constraints that link traits together is the linchpin of our framework. In particular, we argue that tradeoff-breaking events represent a mark of significant evolutionary innovation towards individuality at the higher level that might be missed by fitness-centred approaches.

Appendix 1

Glossary

Particles or cells: The lower-level entities of a two-level biological system.
Collectives or multicells: The higher-level entities of a two-level biological system.
Evolutionary transition in individuality (ETI): Evolutionary process during which collective-level entities become evolutionary individuals and are able to participate in the process of evolution by natural selection ‘in their own right’.
Fitness: The expected average exponential growth rate of a given type of individual (i.e., individual sharing the same traits) in a given steady-state reference environment.
Fitness-decoupling observation: The observation that the fitness of particles decreases while the fitness of collectives increases. Used in the literature as a probable hallmark of an ETI.
Within-collective particle fitness: The fitness of a particle within the collective environment, ignoring collective-level events (e.g., because they happen over a longer timescale). Noted in the main text.
Counterfactual particle fitness: The fitness of a hypothetical particle with the same traits as the actual particle that would live in a non-collective reference environment. There is no unique way to define the counterfactual reference environment. Noted in the main text.
Whole life cycle particle fitness: The fitness of a particle computed over a reference environment that includes the whole life cycle of collectives (including collective birth–death events). Mathematically equal to the collective-level fitness if the collective stage distribution reaches a steady state (i.e., collectives do not keep getting bigger or smaller) as proven in Section 2. Noted in the main text.
Export-of-fitness model: A model used to explain fitness-decoupling observations by a ‘transfer of fitness’ from the particle level to the collective level during ETIs. We treat the terms ‘fitness transfer’ and ‘fitness decoupling’ (when referring to the interpretation not the observation) as equivalent to ‘export of fitness’.
Tradeoff model: An alternative model to the export-of-fitness model used to explain fitness-decoupling observations by invoking ecological or genetic constraints on the values of traits that contribute to counterfactual and whole life cycle fitness during an ETI.
Tradeoff-breaking observation: The observation that some lineages do not seem to conform to the fitness-decoupling observation during an ETI—they show an increase of both counterfactual or within-collective fitness and collective fitness.
Tradeoff-breaking model: A model where the evolutionary trajectories follow constraints that come from the unicellular ancestors (tradeoff) and that include rare phenotypic changes that are not submitted to the same constraints (tradeoff breaking). This model can account for both fitness-decoupling and tradeoff-breaking observations during ETIs.

Data availability

The code implementing the models is publicly available on Zenodo (https://doi.org/10.5281/zenodo.5352208). For Figure 1: Protocol described and statistical analysis performed in Hammerschmidt et al. (2014). Dataset published as Rose et al. (2018). For Figure 6b: Data taken from Colon-Lopez et al. (1997); Mohr et al. (2013); Misra & Tuli (2000); Berman-Frank et al. (2001); Popa et al. (2007) and standardised. For Figure 6c: Data taken from the dataset published as Rose et al. (2018).

The following previously published data sets were used

(2018) Zenodo
ID 3748416#.YxXSi-zML0r. Meta-population structure and the evolutionary transition to multicellularity.

https://zenodo.org/record/3748416#.YwTOaOzML0q

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Decision letter

Will Ratcliff

Reviewing Editor; Georgia Institute of Technology, United States
Patricia J Wittkopp

Senior Editor; University of Michigan, United States
María Rebolleda-Gómez

Reviewer; University of California, Irvine, United States
Matthew Herron

Reviewer; Georgia Institute of Technology, United States
Corina E Tarnita

Reviewer; Princeton University, United States

Our editorial process produces two outputs: (i) public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.

Decision letter after peer review:

Thank you for submitting your article "Beyond Fitness Decoupling: Tradeoff-breaking during Evolutionary Transitions in Individuality" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Patricia Wittkopp as the Senior Editor. The following individuals involved in review of your submission have agreed to reveal their identity: María Rebolleda-Gómez (Reviewer #1); Matthew Herron (Reviewer #2); Corina E Tarnita (Reviewer #3).

The reviewers have discussed their reviews with one another, and the Reviewing Editor has drafted this to help you prepare a revised submission.

Essential revisions:

Fitness decoupling is an important topic that has created a lot of confusion in the field over the last decade and a half. Work clarifying this topic, and moving beyond looking at fitnesses, is welcome and important. The authors are well-poised to write this paper, bringing together real strength in the philosophy of biology, mathematical modeling, and experimental evolution of multicellularity. The modeling framework used here is useful, showing that cell and group-level fitnesses cannot be decoupled when they are both assessed over the same time scale. I agree with referee 3 that it is great to see the authors wrestling with real world data, and not relying only on simple mathematical models, because a key piece of the utility of this kind of theory will rely on people being to apply it to empirical systems. I also agree with the authors that traits, not just fitnesses, can be useful in determining when an ETI has occurred. Moving into traits, the authors propose to focus on trade-off breaking as an indicator that an ETI has occurred, which is creative and potentially quite useful, though further clarification will be required.

The referees raised several important points that will need to be addressed in the revision.

1) As Referee 1 points out, the idea that cell and group-level fitnesses cannot be formally decoupled was noted by Michod in his 2005, 2014, and 2020 papers. While I do not think that Michod has been entirely clear on this, his 2020 paper makes this point unambiguously. I think there's room for grace here with respect to what Michod thinks, and I'd like to avoid un-necessary strawman arguments. I don't think we should conflate Michod's views on this with Okasha's, and should give credit to Michod for accepting that cell and group-level fitness are inexorably correlated. But perhaps more importantly, the conclusion that in simple mathematical models cell and group-level fitnessess cannot be decoupled is not itself novel: Dr. Bourrat himself published this result as the central message of his 2015 paper on fitness decoupling (Bourrat, "Levels, time and fitness in evolutionary transitions in individuality". Philosophy and Theory in Biology). So I'd recommend modifying the language in the manuscript here around whether this is a novel finding (i.e., 2nd lead sentence of the discussion: "Our first main finding is the impossibility of decoupling between commensurable measures of fitness".).

2) I think the main contribution of this paper is the shift from focusing on fitnesses to traits. Specifically, the authors advocate for the concept of trade-off breaking as an indication that an ETI has occurred. I like this idea, in part because it is far easier to measure traits than fitnesses in real organisms. However, the referees have raised some important issues with this idea that should be addressed during revision. As Referees 1 and 2 pointed out, organisms evolve trade-off breaking traits all the time without affecting biological individuality. I thought Referee 1's example of the zebra herd foraging trait was quite effective here, illustrating how collective-behaviors that break trade-offs may be not meaningfully affect the level of biological individuality.

Most importantly, I'd like to see this idea developed a bit more to describe the conditions under which trade-off breaking is an indication of an ETI. Specifically, I'd like the authors to clarify: (1) Is every case of trade-off breaking a case of an ETI? (2) If not, are all ETIs characterized by trade-off breaking? Or (3) Is trade-off breaking one possible way of driving an ETI, but not a universal trait of ETIs? (4) If the latter is true, and trade-off breaking is not necessary or sufficient to distinguish an ETI, then what else is needed to distinguish an ETI? The authors have made a compelling case that the fitness decoupling literature has significant problems, but it is not yet clear that trade-off breaking is the solution.

To clarify my thinking on this a bit more: trade-off breaking seems like a useful tool when there are clear trade-offs that can be ameliorated by multicellular adaptation (for example, by cellular differentiation- the cyanobacterial example is a good one). But what about a case of simple multicellular adaptation in the absence of pre-existing trade-offs? For example, consider a simple organism like a snowflake yeast that is obligately multicellular, reproducing by group fragmentation. Over generations, cells evolve novel traits that improve the fitness of cells living in multicellular groups, but these traits reduce the growth rate of cells. It's easy apply the counter-factual approach and see how the same traits increase the fitness of groups and the cells living in these groups, while decreasing the counterfactual fitness of solitary cells (they grow slower). To me, this is a straightforward use of the counterfactual fitness approach, in line with what Michod suggests in their 2020 paper, and is indicative of an ETI in progress. This isn't hypothetical, it's precisely what we see in snowflake yeast (see Bozdag et al., 2021 Nature Comms for some published data, but we have much more work done in this area that is unpublished). I don't think our model system is very unusual here, and I would think that this kind of simple group-level adaptation is common during the transition to multicellularity.

Thus, the 3 referees and I agree that it is essential that the authors clarify whether trade-off breaking is a universal trait of ETIs, or is one potential diagnostic trait that an ETI has occurred. If it is not universal (which is what we suspect at this point, and claims of universality would require new, compelling arguments), then it would be useful to outline the conditions under which one might want to use a trait-based argument (i.e., trade-off breaking) vs. a fitness-based argument (i.e., counterfactual fitness). The referees and I generally thought that trade-off breaking could be a useful tool for determining that an ETI has occurred, even if it is not a diagnostic feature of all ETIs.

3) Referee 3 points out that the model developed in this paper is not itself novel, being similar in structure and analysis to her prior work. Please cite/discuss this prior work appropriately.

Reviewer #2 (Recommendations for the authors):

Figure 2 would be more useful if it included a comparison of fitnesses, for example between different genotypes (in other words, if it compared particle- and collective-level fitnesses of two genotypes and showed that they are identical if measured over the same time span).

Reviewer #3 (Recommendations for the authors):

Let me start by saying the I am sympathetic to the authors' position on fitness decoupling, which I've always found to be so contrived as to be either non-sensical or meaningless, depending on how one defines fitness. I also quite like the simple proposals of sections 3 and 4 and appreciate that the authors engaged both with empirical evidence and with ways to see existing theoretical models through the lens of the tradeoff-breaking framework. This being said I have a few concerns that I would like addressed:

1. the writing is fairly dense and convoluted: it took me several hours to go through the manuscript, and I'm still unsure that I'm fully grasping all details. If this is going to be engaged with by a broad audience, and especially a non-specialist one, the authors need to make more of an effort to clean up, streamline, and provide intuition. For instance,

– I can't make sense of Figure 4 I don't know which ones of the dots are particles; I don't know which is the focal particle whose fitness we are tracing, I don't understand what the vertical dotted lines are, and I don't know why there are multiple horizontal lines, seemingly associated with both blue and orange dots. This lack of clarity around exactly how to measure f2 and F propagate, making it sort of hard to rigorously understand what the authors meant f2 to be in various of the examples (though, in principle, if I don't worry too much about understanding Figure 4, I can follow what f2 in principle might be in each example, as needed).

– I found it tedious to go through all the math derivations and references to theorems in the main text, with, often, little to nothing by way of biological intuition that would help ground some of those results. When some biological intuition is provided, it often left me wanting some more explanation. For instance, in discussing the example of section 3.3, the authors state: "Note importantly that the opposite directions of the dynamics of F and f2 is a consequence not a cause of the underlying tradeoff mechanism that drives the evolutionary dynamics." It would be great if the authors could explain why this is; and, in general, this whole example could use a bit of biology on the very bare theoretical bones. For example, it seems that all collectives of size i >= 2 have the same survival probability and the same probability to grow to the next class size; if the authors can't contextualize this with a bit more biology, at the very least it would be nice to have a sentence that simply states this assumption in words. A non-mathematical reader might have a hard time inferring that from the fact that the expressions of p_i and g_i don't depend on i.

– Although I understand the tradeoff in Black et al., I'm still not entirely sure I understand the tradeoff in the model in Box 2: is there supposed to be a tradeoff linking β and q? It seems that β is a growth rate whose increase would be good for both germ cells and soma cells. In both Boxes 2 and 3 it would be helpful to have it more clearly spelled out which modeling aspects are new to this paper and which ones are taken from the original papers, which were themselves modeling papers.

– Simultaneously, some things that are simple to state intuitively, are presented in a somewhat convoluted and tedious way: e.g., the 1st paragraph of Box 1 and associated Figure B1a make overly complicated the story that any reader would appreciate with a simple example: a bacterium that doubles every hour will make more of itself in one year than a mouse that "doubles" every year (or interest compounding or a suite of other simple, intuitive examples). I also think that some such intuitive discussions should come earlier, as the authors set up the discussion of fitness in the main text (prior to Figure 4).

– In general, I'm not convinced that some of the mathematical detail needs to be in the main text as opposed to a detailed methods section.

2. The model in Section 2 is not new. Tarnita et al. 2013 J. Theor Biol (Evolutionary construction by staying together and coming together) have used the same model to explore the origin of multicellularity. Even though that paper looks at competition of such collectives against the solitary ancestor, the ideas, setup and analyses are nearly identical to what the authors do in section 2.

3. This brings me to my final and broadest points:

– First, if I understand correctly, in this manuscript Bourrat et al. do not seem to consider competition against an extant unicellular ancestor anymore. But, it seems to me that one of the greatest challenges would've been the persistence of the multicellular lifestyle in the earliest stages, before rare mutations can break tradeoffs and whatnot. It would be useful to at least have some discussion of this early on, so that I can situate where exactly the modeled worlds are in the origin of multicellularity and transition to individuality (i.e. what is assumed to have happened already, vs what is the new challenge to be explained).

– Second, how should we think of free riders in this framework? They don't seem to be explicitly included in any of the modeling.

– Third, much as in the original Michod thinking, it seems to me that the current framework also sort of assumes that the collective is a sum of what the component cells do and does not consider spontaneous emergent properties that simultaneously confer benefits of group living on the group and also on the parts, such as some degree of division of labor [that harnesses the repertoire of the unicellular ancestor and arises e.g., due to emergent information gradients in the earliest collectives]. Such spontaneous benefits could in themselves set the stage for an ETI without requiring fundamental reversals of tradeoffs (even though these of course could follow later). Again, I'm not suggesting that the current framework should be explicitly modified to account for such dynamics, but it would be informative to have at least some discussion of whether the authors believe that tradeoff-breaking by rare mutations is the only way to get an ETI or whether it's one possible thing to look for empirically, but not necessarily the only route.

To contextualize this point further, it might be helpful to look at Ulrich et al. 2018 Nature (Fitness benefits and emergent division of labour at the onset of group living) and Brahma et al. 2017 (Emergence of cooperation and division of labor in the primitively eusocial wasp Ropalidia marginata). Both of these look at the evolution of eusociality rather than multicellularity, but the essence of the ETI can be captured by the same model (see, Tarnita et al. 2013). I'm not aware of similar empirical work in multicellularity, though see Gavrilets 2010 PLoS Comp Biol (Rapid Transition towards the Division of Labor via Evolution of Developmental Plasticity) for theoretical work.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "How Tradeoff-Breaking Events Go Beyond Fitness Decoupling During Evolutionary Transitions in Individuality" for further consideration by eLife. Your revised article has been evaluated by Patricia Wittkopp (Senior Editor) and a Reviewing Editor.

The three referees and I have read your revised manuscript, and really appreciate some of the new additions. In particular, there is a lot of enthusiasm for the new Section 5. Everyone found the paper to be thought-provoking and thought that this paper will make an important contribution to understanding ETIs if suitably revised.

The main thing we would like to suggest is a more inclusive tone for the paper. I do not think it takes away any of the novelty of the results, and indeed, can strengthen the scholarship of the work. It is critical that you revise the introduction to more fairly reflect Michod et al.'s stated meaning (not the authors' inferred meaning) about the concepts of export of fitness, fitness decoupling, and the counterfactual account. Second, the referees and I do not see why the counterfactual account is not a valid indicator that an ETI has occurred. This does not undercut the utility of your work, showing that trade-off breaking mutations can be an indication of an ETI. But all four of us are convinced that both approaches have merit.

Referee 2 has left a detailed review, highlighting five major points. The referees and I agree that it is essential to address all five points with changes to the MS, not arguments for why revision is not necessary. Please respond to their review thoroughly. I have carried forward their five summary points and provided a bit of additional context on some below, reflecting our collective post-review discussion.

1. Adequately address Michod and colleagues' "counterfactual fitness" interpretation of their own model or give a compelling reason not to in the manuscript.

Despite pointing this out in the last revision, the paper still does not treat Michod et al.'s position on fitness decoupling and counterfactual fitness fairly. The paper is framed in such a way that it critiques a straw-man version of Michod et al's position on these topics (privileging the authors' interpretation of what Michod et al. have said, or what the metaphor of "fitness decoupling" implies), which stands in contrast to what Michod and colleagues have explicitly said they mean by these terms in their more recent papers.

2. Make a compelling case for the lack of utility of the counterfactual fitness version of fitness decoupling in the manuscript or remove this claim from the manuscript.

Given that you are using a Darwinian Individuality approach to define what is an individual (clearly defined in the glossary, thank you!), I do not see how one can dismiss the utility of the counterfactual fitness approach. Empirical measures consistent with the counterfactual fitness account can provide insight into whether groups have been acting as Darwinian Individuals. For example, consider a lineage evolving along a pre-existing trade-off between traits that improve the fitness of groups and those that improve the fitness of cells, like those identified in Figure 8's depiction of 'optimization on the trade-off'. Using the example given in this section, consider the mutations that make snowflake yeast cells elongate, which increase group size (and thus fitness) but decrease cell growth rates (and thus fitness). This would be detected in the counterfactual fitness account and would rightly be interpreted as a trait that evolved due to selection acting among groups, not among individual cells, demonstrating that groups are Darwinian Individuals. Trade-offs have not been broken, but nonetheless, groups replicate, have heritable variation in group-level traits, and selection acts on those traits, resulting in adaptations that would not have occurred among unicellular populations. I think we can all agree that in this case, measurements consistent with the counterfactual approach would indicate that groups are a Darwinian Individual according to PGS's criteria, right? On a related note, I couldn't figure out why the MS embraced the 'Ratcheting' model but rejected the counterfactual account since ratcheting is based on the same trade-offs that would be detected by the counterfactual fitness account.

However, I think your paper raises very valid limitations on the scope of counterfactual fitness- not all multicellular adaptations will necessarily create a trade-off between fitness in groups and fitness in isolated cells, reverting lineages to unicellularity may often prove impossible, and measuring fitness can be difficult, etc. From my perspective, both the counterfactual fitness account and the trade-off breaking account may be useful indicators that an ETI (following the Darwinian Individuality criteria) has occurred. And importantly, I do not think either is necessary or sufficient to show an ETI has occurred without additional information about the traits themselves. They both require context to be informative.

Since neither is necessary for an ETI, a lineage may evolve along either route (or both simultaneously, as they are not mutually exclusive). I could imagine cases where it is much easier to identify trade-off breaking mutations and others where it is easier to identify counterfactual fitness. Having both tools available is a net positive for our field, and I don't see the need to limit ourselves only to tradeoff-breaking mutations. All the more so if trade-off breaking mutations are not necessary or sufficient to show an ETI, making the decision to only consider them somewhat arbitrary.

3. Consistently describe what is and is not novel about the finding of incommensurability.

This is described clearly in the original review and I have no additional context to add.

4. Consistently acknowledge that trade-off breaking is insufficient as a marker for an ETI.

As acknowledged in the prior review, trade-off breaking is not sufficient to determine that an ETI has occurred. It is possible to have a trade-off-breaking mutation occur within a single level. The referees and I agree that the MS should be consistent about this limitation and avoid saying the existence of that trade-off breaking mutations mean an ETI has occurred. To this end, it would be very helpful if the authors could identify what additional information one would need to know in order to conclude that a trade-off breaking trait indicates that an ETI has occurred (i.e., it's pretty clear if the adaptation derives from cellular differentiation in a way that overcomes cell-level trade-offs, like C and N fixation in cyanobacteria, but what about other kinds of adaptations? How would one infer that adaptations generating novel multicellular morphology are breaking trade-offs? What if the adaptations in question do not stem from the limitations of the unicellular ancestor [i.e., those that are limited by trade-offs], but rather reflect the novel ecology and behavior of the multicellular organism?).

5. Clarify, in the manuscript, how the dynamics of F and f2 fail to explain the dynamics described in lines 407-417.

This is described clearly in the original review and I have no additional context to add.

Reviewer #1 (Recommendations for the authors):

This paper will be an important read for everyone interested in discussions about fitness, transitions in individuality, and innovations more broadly. It helpfully pushes the conversation away from fitness and into understanding the underlying traits.

This revised version frames the argument better within its context in the previous literature, and it does a good job of clarifying central points that were hard to follow in the previous version. Figure 8, the new discussion of the snowflake yeast example, and the added text at the end of the trade-off breaking section add clarity and set the boundaries of what is and what isn't explained by this framework.

Reviewer #2 (Recommendations for the authors):

The revised manuscript largely fails to adequately address the central criticisms in my review of the original manuscript. Reasons for this are given in the authors' response, but these responses are inadequate for the reasons detailed below.

1. In my review of the original manuscript, I suggested that the manuscript did not fully address Michod and colleagues' description of their fitness decoupling models in terms of "counterfactual" fitness ("the impression conveyed is that Michod and colleagues consider decoupling of "commensurably computed fitnesses" possible, which is counter to their explicit statements on the topic."). The revised version still does not. Counterfactual fitness is not introduced at all until Section 2.3, so the Introduction and much of the Results read as if Michod and colleagues had never clarified that this is how their fitness decoupling models should be understood, and the authors' preferred interpretation, was explicitly rejected by Michod and colleagues, is central to the manuscript's framing. The authors' response gives some (inadequate) rationale for largely ignoring Michod and colleagues' preferred interpretation of their own model, but this rationale is not included in the manuscript. The reason I say the rationale is inadequate is that it privileges the authors' interpretation (what the "metaphor implies") over Michod and colleagues' explicit, repeated, published explanations of their own model. If the authors wish to frame the manuscript in terms of a version of Michod and colleagues' model that Michod and colleagues themselves say is mistaken, an adequate justification for doing so should be included in the manuscript.

2. In my review of the original manuscript, I said that "the final assessment (Section 2.3) does not make a compelling case for its central argument, the lack of utility of the fitness decoupling concept." The relevant section (actually 2.4) still does not make a compelling case that the fitness decoupling concept lacks utility. The reason given is "because they [F and f1/f2] are not commensurable." Since commensurability of F and f2 is not part of Michod and colleagues' formulation of fitness decoupling, this is not a compelling reason. As I said in my original review, "…'because they are not commensurable' does little to explain why the counterfactual interpretation of fitness decoupling 'does little on its own to clarify the process of an ETI,' since commensurability is not a claim that the counterfactual interpretation of fitness decoupling makes." The authors' response is inadequate for reasons I have touched on before (privileging the authors' interpretation over Michod and colleagues' explicit description of their own model), and the manuscript has not been modified to address this point.

3. The Review Editor points out that "the conclusion that in simple mathematical models cell and group-level fitness cannot be decoupled is not itself novel", and the authors' response acknowledges "this idea has already been developed in the literature"; however:

– The Abstract reads (lines 34-37) "Using a mathematical approach, we show this concept to be problematic in that the fitness of particles and collectives can never decouple-calculations of particle and collective fitness performed over appropriate and equivalent time intervals are necessarily the same." The Abstract reads as if this were a novel finding of this work, which it is not.

– Similarly, lines 95-97 and 109-110 suggest the novelty of this result.

– Lines 190-191 read "While fitness decoupling and the export-of-fitness model might seem useful concepts for understanding ETIs, we show formally here that commensurably computed fitnesses cannot generally be decoupled." Again, this sounds like a novel result, which it is not. The subsequent sentences provide some context but do not acknowledge that Michod derived this result in 2005. It may be that the authors intend some distinction from prior results as suggested in the authors' response (e.g. that they were not shown "formally" or "generally"), but this distinction is not clear in the manuscript. What is novel about this result and how it differs from prior results (including the formal analysis of Shelton & Michod 2014) will need to be clarified in the manuscript.

4. The authors' response acknowledges that "tradeoff-breaking events cannot be regarded as sufficient conditions for an ETI", and the revised manuscript acknowledges (line 654) that "…a tradeoff-breaking event in and of itself cannot be used as a marker of an ETI." However:

– The Abstract (line 42) reads “tradeoff-breaking stands as a useful marker for ETIs,”.

– Line 537 that "…tradeoff-breaking observations are the mark of significant genetic innovation and, thus, can be used as a hallmark of ETIs,".

– Lines 417-418 that "…one genuine marker for an ETI is the capacity for a lineage to break away from such a tradeoff,".

– Lines 669-670 that "a general marker of ETIs to use in lieu of fitness decoupling is the emergence of rare tradeoff-breaking mutations."

– Lines 687-689 suggest that trade-off breaking is superior to fitness decoupling because "a fitness decoupling observation is not a reliable marker that an ETI is occurring". Since trade-off breaking is also not a reliable marker that an ETI is occurring, the point of this contrast is unclear.

5. I do not see how the conclusion that "…relative changes in fitness F and f2 do not explain the dynamics observed" follows from the rest of the paragraph (lines 407-417).

– For example, "the opposite directions of the dynamics of F and f2 are a consequence of optimal trait values on a tradeoff being different in different environments, not an inherent relationship between them" describes Michod's models neatly, with the dynamics of group fitness (F) and counterfactual fitness (f2) being a consequence of optimal trait values (investment in fecundity, investment in viability) being different in different environments (within the group versus outside the group). This seems to be an example, not a counterexample, of relative changes in fitness in F and f2 explaining the dynamics observed.

– In the snowflake yeast example, "f2 decreases…when wholeLife cycle fitness F increases" again seems to be an example of relative changes in fitness in F and f2 explaining the dynamics observed, but it is presented as a counterexample. Trade-offs and fitness decoupling in the counterfactual sense are not mutually exclusive explanations; the fact that trade-offs are involved, as in Michod's fitness decoupling models, does not mean fitness decoupling in the counterfactual sense is not occurring.

Recommendations for authors

These have a 1:1 correspondence with the items above

1. Adequately address Michod and colleagues' "counterfactual fitness" interpretation of their own model or give a compelling reason not to in the manuscript.

2. Make a compelling case for the lack of utility of the counterfactual fitness version of fitness decoupling in the manuscript or remove this claim from the manuscript.

3. Consistently describe what is and is not novel about the finding of incommensurability.

4. Consistently acknowledge that trade-off breaking is insufficient as a marker for an ETI.

5. Clarify, in the manuscript, how the dynamics of F and f2 fail to explain the dynamics described in lines 407-417.

Reviewer #3 (Recommendations for the authors):

I really enjoyed reading the revised manuscript, especially the newly-added Section 5. I think everything is much clearer now, and although parts and ideas have been discussed elsewhere, bringing them together in a coherent conceptual and theoretical framework is novel and useful. It certainly got me thinking in directions that I hadn't previously considered.

I have only one final comment. I appreciate the idea of separating the stage of collective formation from the subsequent ones and the authors' clarification that they focus on the latter (and hence that they choose not to focus on the competition with unicellular ancestors). But what if some collective property is needed precisely to overcome the competition with the unicellular ancestor? That's certainly how the experiments in Ulrich et al. 2018 came about: because in a model similar to the one in Tarnita et al. 2013 but published in the context of eusociality in Nowak et al. 2010, we predicted that a necessary condition for eusociality to evolve was for per capita fitness to get a drastic boost at very small, incipient group sizes, without any time for additional mutations. And in 2010 we had no clue what that could be. In 2018 we showed experimentally that spontaneous, rudimentary division of labor could do it.

In other words, one might sometimes be in a situation where Stage 2 is altogether skipped precisely because only collectives that snap right into some form of Stage 3 already during stage 1 can outcompete the ancestor. Put differently, Stage 1 = Stage 3.

Again, it seems to me that there are many ways to skin a cat and the authors are making it clear now that rare mutation doesn't have to be the only route to an ETI, but that some overarching framework based on traits and tradeoffs might offer a more productive way to look broadly at ETIs. I just wanted to alert them to the possibility that tradeoff breaking might not necessarily always occur after Stage 1 (and the associated competition with the ancestor) but sometimes might even occur during it. Unless I'm missing something?

https://doi.org/10.7554/eLife.73715.sa1

Author response

Essential revisions:

Fitness decoupling is an important topic that has created a lot of confusion in the field over the last decade and a half. Work clarifying this topic, and moving beyond looking at fitnesses, is welcome and important. The authors are well-poised to write this paper, bringing together real strength in the philosophy of biology, mathematical modeling, and experimental evolution of multicellularity. The modeling framework used here is useful, showing that cell and group-level fitnesses cannot be decoupled when they are both assessed over the same time scale. I agree with referee 3 that it is great to see the authors wrestling with real world data, and not relying only on simple mathematical models, because a key piece of the utility of this kind of theory will rely on people being to apply it to empirical systems. I also agree with the authors that traits, not just fitnesses, can be useful in determining when an ETI has occurred. Moving into traits, the authors propose to focus on trade-off breaking as an indicator that an ETI has occurred, which is creative and potentially quite useful, though further clarification will be required.

The referees raised several important points that will need to be addressed in the revision.

1) As Referee 1 points out, the idea that cell and group-level fitnesses cannot be formally decoupled was noted by Michod in his 2005, 2014, and 2020 papers. While I do not think that Michod has been entirely clear on this, his 2020 paper makes this point unambiguously. I think there's room for grace here with respect to what Michod thinks, and I'd like to avoid un-necessary strawman arguments. I don't think we should conflate Michod's views on this with Okasha's, and should give credit to Michod for accepting that cell and group-level fitness are inexorably correlated. But perhaps more importantly, the conclusion that in simple mathematical models cell and group-level fitnessess cannot be decoupled is not itself novel: Dr. Bourrat himself published this result as the central message of his 2015 paper on fitness decoupling (Bourrat, "Levels, time and fitness in evolutionary transitions in individuality". Philosophy and Theory in Biology). So I'd recommend modifying the language in the MS here around whether this is a novel finding (i.e., 2nd lead sentence of the discussion: "Our first main finding is the impossibility of decoupling between commensurable measures of fitness".).

Essential revision #1 concerns the novelty of the idea that commensurable measures of fitness cannot be decoupled and our treatment of previous publications in the domain. We do agree with the reviewers that this idea has already been developed in the literature and that a better description of our specific contribution is to add a new formal argument supporting this claim through mathematical modelling (something that was not done in Bourrat, 2015, for instance) and under more general conditions (i.e., we do not only address ‘simple models’ but all models that reach a stable collective size distribution).

Our intention is in no way to create strawman arguments. We agree that Michod and collaborators have clarified their position in several publications. In particular, we recognise that they (1) mention that particle and collective fitness must be correlated and (2) judiciously introduce counterfactual fitness to solve this problem. However, we argue that the export-of-fitness metaphor implies that the two quantities between which a fitness transfer occurs are commensurable. As a result, we think that the export-of-fitness model is incompatible with the use of counterfactual fitness (see our response to Reviewer #3’s public review for more details).

In light of this comment, we made the following changes to the manuscript:

We edited the wording in several places to distinguish the contributions of Michod and Okasha. We note that Okasha relies extensively on Michod and colleagues’ work to propose his three-stage model.
In the glossary, we removed the mention of counterfactual fitness being a ‘recent development” in the export-of-fitness literature.
In the introduction and Section 1, we clarified that our argument about fitness decoupling is to show formally its impossibility under reasonable assumptions, which is a novel contribution and not covered in Bourrat (2015).
In the discussion, we replaced ‘Our first main finding is the impossibility of decoupling between commensurable measures of fitness’ with ‘Our first main finding is a new formal argument cementing the position holding that decoupling between commensurable measures of fitness is impossible’.

2) I think the main contribution of this paper is the shift from focusing on fitnesses to traits. Specifically, the authors advocate for the concept of trade-off breaking as an indication that an ETI has occurred. I like this idea, in part because it is far easier to measure traits than fitnesses in real organisms. However, the referees have raised some important issues with this idea that should be addressed during revision. As Referees 1 and 2 pointed out, organisms evolve trade-off breaking traits all the time without affecting biological individuality. I thought Referee 1's example of the zebra herd foraging trait was quite effective here, illustrating how collective-behaviors that break trade-offs may be not meaningfully affect the level of biological individuality.

Most importantly, I'd like to see this idea developed a bit more to describe the conditions under which trade-off breaking is an indication of an ETI. Specifically, I'd like the authors to clarify: (1) Is every case of trade-off breaking a case of an ETI? (2) If not, are all ETIs characterized by trade-off breaking? Or (3) Is trade-off breaking one possible way of driving an ETI, but not a universal trait of ETIs? (4) If the latter is true, and trade-off breaking is not necessary or sufficient to distinguish an ETI, then what else is needed to distinguish an ETI? The authors have made a compelling case that the fitness decoupling literature has significant problems, but it is not yet clear that trade-off breaking is the solution.

To clarify my thinking on this a bit more: trade-off breaking seems like a useful tool when there are clear trade-offs that can be ameliorated by multicellular adaptation (for example, by cellular differentiation- the cyanobacterial example is a good one). But what about a case of simple multicellular adaptation in the absence of pre-existing trade-offs? For example, consider a simple organism like a snowflake yeast that is obligately multicellular, reproducing by group fragmentation. Over generations, cells evolve novel traits that improve the fitness of cells living in multicellular groups, but these traits reduce the growth rate of cells. It's easy apply the counter-factual approach and see how the same traits increase the fitness of groups and the cells living in these groups, while decreasing the counterfactual fitness of solitary cells (they grow slower). To me, this is a straightforward use of the counterfactual fitness approach, in line with what Michod suggests in their 2020 paper, and is indicative of an ETI in progress. This isn't hypothetical, it's precisely what we see in snowflake yeast (see Bozdag et al., 2021 Nature Comms for some published data, but we have much more work done in this area that is unpublished). I don't think our model system is very unusual here, and I would think that this kind of simple group-level adaptation is common during the transition to multicellularity.

Thus, the 3 referees and I agree that it is essential that the authors clarify whether trade-off breaking is a universal trait of ETIs, or is one potential diagnostic trait that an ETI has occurred. If it is not universal (which is what we suspect at this point, and claims of universality would require new, compelling arguments), then it would be useful to outline the conditions under which one might want to use a trait-based argument (i.e., trade-off breaking) vs. a fitness-based argument (i.e., counterfactual fitness). The referees and I generally thought that trade-off breaking could be a useful tool for determining that an ETI has occurred, even if it is not a diagnostic feature of all ETIs.

Essential Revision #2 concerns the generality of the tradeoff-breaking mechanism for the study of ETIs and asks us to detail our framework in the examples of the zebra herd and the snowflake yeast. We will start by answering the first set of concerns: the example of the zebra herd is addressed in our detailed answer to Reviewer #2 and we will come back to the snowflake yeast later.

As pointed out by the reviewers, we hope first and foremost that this manuscript will contribute to shifting the field from focusing on fitness to focusing on traits. We are motivated in this endeavour by our conviction that we, as a field, have reached the limits of what we can learn from fitness-based approaches to ETIs. One of the undeniable appeals of the export-of-fitness model is that it can be applied in the abstract without taking into account the likely very particular underlying constraints of the system. However, this constitutes a double-edged sword—when the assumptions of the export-of-fitness model are not met, the theory cannot account for the dynamics observed. This is so because, to expect a dynamic in which counterfactual fitness decreases and whole life cycle fitness increases, one must assume three things. First, the two quantities must depend upon the same traits; second, these two quantities are maximised for different trait values; third, the ancestral trait values (as the product of previous selection on the unicellular ancestor) correspond to the maximum of counterfactual fitness within the constraints of the ancestor. In contrast, if traits and tradeoffs are the centre of the theory, not only are all previous results about counterfactual fitness and ratcheting valid (albeit not explained using the metaphor of fitness transfer) but also tradeoff-breaking events—which occur when the three above assumptions do not hold—can be accommodated readily.

However, the reviewers are correct in their assessment that we did not discuss sufficiently the generality of the fitness tradeoff-breaking approach. First, if one takes the idea of tradeoff breaking in its broadest sense—that is, the emergence of rare mutations that overcome the usual constraints bearing upon a set of traits—we agree with the reviewers that tradeoff-breaking events cannot be regarded as sufficient conditions for an ETI. This is so because tradeoff breaking might occur without being accompanied by a change in the level of individuality. (Note that this is also the case with fitness-decoupling observations. Counterfactual fitness might decrease in a population of particles where particles interact with one another and must be surrounded by other particles to survive without this population producing higher-level individuals.) However, we suggest that it could tentatively be proposed as a necessary condition for the evolution of individuality. Several models of ETIs involve a first step of collective formation followed by collective level changes (e.g., Bourke, 2011; van Gestel & Tarnita, 2017; Rose & Hammerschmidt, 2021)—that is, a way to assemble lower-level entities in stable collectives—and secondary changes that cement the individuality of the new collectives. Tradeoff-breaking could be used as a practical way of assessing this second step, characterising what differs from collectives exhibiting low or little interaction (e.g., herds of deer, to take a famous example) and, thus, forming a necessary condition for a complete ETI.

The question of the snowflake yeast system is of particular interest to us. However, to treat the topic with the respect it deserves would require a detailed treatment that would go beyond the scope of this article. Nonetheless, we can make the following conjecture: the first snowflake mutation (ACE2) acts as the ‘collective formation‘ mutation (step one, similar to the WS mutation in the Pseudomonas system). From then, the observed change in cell shape (day 4 to 65 in the original experiments described in Ratcliff et al., 2012, 2013, 2014) fits well with the ‘optimisation on the tradeoff’, as we conceptualise it. As explored by Bozdag et al. (2021), the bigger clusters suffer from poorer oxygenation of the cells reducing the cell growth rate, which means that the increase in cluster size is accompanied by a reduction in within-collective particle growth rate (f₁). A more delicate experimental question would be to establish whether the following recorded innovations (the changes in cluster shape in days 65–227 described in Ratcliff et al., 2013; the increased apoptosis described in Ratcliff et al., 2014; Jacobsen et al., 2018; or even the snowflakes aggregates described in Gulli et al., 2019) constitute a proper ‘tradeoff breaking‘ as we describe it in the article. One way to explore this would be to combine the existing data on cell and cluster shape (Ratcliff et al., 2012, 2013, 2014), physical models of cluster volume (Libby et al., 2014; Jacobsen et al., 2018), simple sedimentation models (as used in Solari et al., 2015), and within-flake cell growth models (Bozdag et al., 2021) and give the snowflake system the same transversal treatment that we give the Pseudomonas system in this article.

In light of these comments, we made the following changes to the manuscript:

We have added a new Section 5 that (1) makes clearer that tradeoff breaking is the second (or third) step in an adaptive scenario that involves ‘collective formation’, ‘optimisation on the tradeoff’ and ‘tradeoff breaking’. To make this effective, we have added a new figure (Figure 8), (2) discussed the generality of the tradeoff approach, and (3) contextualised our approach within the broader picture of ETIs, linking it to the existing framework.
We now include the snowflake yeast system in our examples (in Section 5).

3) Referee 3 points out that the model developed in this paper is not itself novel, being similar in structure and analysis to her prior work. Please cite/discuss this prior work appropriately.

Essential Revision #3 concerns the novelty of the modelling approach. We do agree that we are not the first to have proposed to model proto-collectives using size classes and transition between those size classes (growth, shrinkage, and propagule production). The model can be traced back to an extension of Leslie matrices (Leslie, 1945) and their generalisation as class-based Matrix population models (Caswell 1989). The literature on this topic already makes use of Perron-Frobenius theory to make asymptotic predictions.

Tarnita et al. (2013) present a valuable treatment of the problem using ordinary differential equations and focus on competition with the single-cell counterpart, which we ignored for the purpose of this article. Pichugin et al. (2017) uses a similar dominant eigenvalue method (as we did) to treat the problem of complex fragmentation modes (whereas we only allow single-cell propagules shedding).

In light of these comments, we have better situated our modelling approach with respect to the existing literature by making the following changes:

We added the following references to the paragraph introducing the model (Section 3): Leslie (1945), Caswell (1989), Tarnita (2013), and Pichugin (2017).
We discussed in further detail the fact that we ignore competition with the unicellular ancestor as studied in Tarnita et al. (2013) (Section 5).

Reviewer #2 (Recommendations for the authors):

Figure 2 would be more useful if it included a comparison of fitnesses, for example between different genotypes (in other words, if it compared particle- and collective-level fitnesses of two genotypes and showed that they are identical if measured over the same time span).

We have decided not to change Figure 2, as it is introduced in Section 1 where we have not yet presented the idea that fitnesses measured at the particle and collective level are necessarily equal. We believe this could potentially confuse the reader.

Reviewer #3 (Recommendations for the authors):

Let me start by saying the I am sympathetic to the authors' position on fitness decoupling, which I've always found to be so contrived as to be either non-sensical or meaningless, depending on how one defines fitness. I also quite like the simple proposals of sections 3 and 4 and appreciate that the authors engaged both with empirical evidence and with ways to see existing theoretical models through the lens of the tradeoff-breaking framework. This being said I have a few concerns that I would like addressed:

1. the writing is fairly dense and convoluted: it took me several hours to go through the manuscript, and I'm still unsure that I'm fully grasping all details. If this is going to be engaged with by a broad audience, and especially a non-specialist one, the authors need to make more of an effort to clean up, streamline, and provide intuition. For instance,

– I can't make sense of Figure 4 I don't know which ones of the dots are particles; I don't know which is the focal particle whose fitness we are tracing, I don't understand what the vertical dotted lines are, and I don't know why there are multiple horizontal lines, seemingly associated with both blue and orange dots. This lack of clarity around exactly how to measure f2 and F propagate, making it sort of hard to rigorously understand what the authors meant f2 to be in various of the examples (though, in principle, if I don't worry too much about understanding Figure 4, I can follow what f2 in principle might be in each example, as needed).

We have extensively reworked Figure 4 to make this clearer.

– I found it tedious to go through all the math derivations and references to theorems in the main text, with, often, little to nothing by way of biological intuition that would help ground some of those results. When some biological intuition is provided, it often left me wanting some more explanation. For instance, in discussing the example of section 3.3, the authors state: "Note importantly that the opposite directions of the dynamics of F and f2 is a consequence not a cause of the underlying tradeoff mechanism that drives the evolutionary dynamics." It would be great if the authors could explain why this is; and, in general, this whole example could use a bit of biology on the very bare theoretical bones. For example, it seems that all collectives of size i >= 2 have the same survival probability and the same probability to grow to the next class size; if the authors can't contextualize this with a bit more biology, at the very least it would be nice to have a sentence that simply states this assumption in words. A non-mathematical reader might have a hard time inferring that from the fact that the expressions of p_i and g_i don't depend on i.

We have now provided further explanation and a biological example to address this point.

– Although I understand the tradeoff in Black et al., I'm still not entirely sure I understand the tradeoff in the model in Box 2: is there supposed to be a tradeoff linking β and q? It seems that β is a growth rate whose increase would be good for both germ cells and soma cells. In both Boxes 2 and 3 it would be helpful to have it more clearly spelled out which modeling aspects are new to this paper and which ones are taken from the original papers, which were themselves modeling papers.

In the model from Black et. al, the trait β is more akin to the underlying resource allocation trait that can be seen in other tradeoffs models, such as the trait θ from Section 3 of the main text. It corresponds to the linear abscissa on a 2D tradeoff line. The tradeoff exists in the sense that a collective cannot at the same time have a high initial growth rate β and reach a high collective size at the moment of dispersal, g(T). This tradeoff is broken by mutations on q because somatic cells improve dispersal (if ρ>0) while reducing less the growth rate than mutations on β .

We made the following edits to the boxes:

We explicitly mentioned the parallel between β . (from Black et al.) and θ (in the main text) to clarify the tradeoff involved in this example.
We made more precise references to the original equations,
We added a sentence: ‘we now recast the model within our framework’ to delineate the point where we start to make an original contribution.

– Simultaneously, some things that are simple to state intuitively, are presented in a somewhat convoluted and tedious way: e.g., the 1st paragraph of Box 1 and associated Figure B1a make overly complicated the story that any reader would appreciate with a simple example: a bacterium that doubles every hour will make more of itself in one year than a mouse that "doubles" every year (or interest compounding or a suite of other simple, intuitive examples). I also think that some such intuitive discussions should come earlier, as the authors set up the discussion of fitness in the main text (prior to Figure 4).

We have now streamlined the first section of Box 1 and provided a biological intuition using an example involving bacteria.

– In general, I'm not convinced that some of the mathematical detail needs to be in the main text as opposed to a detailed methods section.

We have decided to keep those details in the main text. However, we provided some signposting at the beginning of Section 2 so that the reader willing to skip the mathematical details can easily do so.

2. The model in Section 2 is not new. Tarnita et al. 2013 J. Theor Biol (Evolutionary construction by staying together and coming together) have used the same model to explore the origin of multicellularity. Even though that paper looks at competition of such collectives against the solitary ancestor, the ideas, setup and analyses are nearly identical to what the authors do in section 2.

Thanks for bringing this to our attention. See our response to Essential Revision #3.

3. This brings me to my final and broadest points:

– First, if I understand correctly, in this manuscript Bourrat et al. do not seem to consider competition against an extant unicellular ancestor anymore. But, it seems to me that one of the greatest challenges would've been the persistence of the multicellular lifestyle in the earliest stages, before rare mutations can break tradeoffs and whatnot. It would be useful to at least have some discussion of this early on, so that I can situate where exactly the modeled worlds are in the origin of multicellularity and transition to individuality (i.e. what is assumed to have happened already, vs what is the new challenge to be explained).

Our main goal is to define a unified framework where different fitness measures that have been used experimentally (e.g., counterfactual particle fitness, within-collective particle fitness, whole–life cycle particle fitness) can be described and their relationship studied in a mechanistic way. In particular, we want to be able to avoid making reference to the export-of-fitness metaphor, on which we share the reviewer’s opinion.

The paper assumes that some early ‘collective formation’ (WS, ACE2, etc.) mutation, or environmental change has already happened and focuses on the early evolutionary dynamics of the proto-multicellular organisms. It also assumes that nascent multicellularity will be constrained by tradeoff inherited from the unicellular ancestors, and that underlying constraints explain in part what has been described as fitness decoupling. However, we advocate that this pattern does not hold as soon as tradeoff-breaking mutations arise (something that presents a challenge for the export-of-fitness view).

In light of this comment, we have added a sentence at the beginning of Section 2 (where we present our model) to state that we do not study the potential competition between particles and protocollectives, as done in Tarnita et al. (2013). We return to this point in Section 5, which also better situates our work with respect to the different phases of an ETI.

– Second, how should we think of free riders in this framework? They don't seem to be explicitly included in any of the modeling.

Free-riders, or cheaters, are not the focus of this model, but could be addressed if necessary using an additional layer of game-theory modelling. We now explicitly mention this at the beginning of Section 2.

– Third, much as in the original Michod thinking, it seems to me that the current framework also sort of assumes that the collective is a sum of what the component cells do and does not consider spontaneous emergent properties that simultaneously confer benefits of group living on the group and also on the parts, such as some degree of division of labor [that harnesses the repertoire of the unicellular ancestor and arises e.g., due to emergent information gradients in the earliest collectives]. Such spontaneous benefits could in themselves set the stage for an ETI without requiring fundamental reversals of tradeoffs (even though these of course could follow later). Again, I'm not suggesting that the current framework should be explicitly modified to account for such dynamics, but it would be informative to have at least some discussion of whether the authors believe that tradeoff-breaking by rare mutations is the only way to get an ETI or whether it's one possible thing to look for empirically, but not necessarily the only route.

We are interested in the same topic as the reviewer here: how the complexity of the repertoire of the unicellular ancestor affects the early collectives. We think that focusing on traits (and tradeoffs) instead of fitness is a necessary step in addressing this question. We do recognise that phenotypic plasticity could play a driving role in this phenomenon, leading to apparent tradeoff breaking without requiring mutations. We have included this possibility in a new paragraph within section 5 (beginning with ‘Yet another possibility not studied in this article is…’).

To contextualize this point further, it might be helpful to look at Ulrich et al. 2018 Nature (Fitness benefits and emergent division of labour at the onset of group living) and Brahma et al. 2017 (Emergence of cooperation and division of labor in the primitively eusocial wasp Ropalidia marginata). Both of these look at the evolution of eusociality rather than multicellularity, but the essence of the ETI can be captured by the same model (see, Tarnita et al. 2013). I'm not aware of similar empirical work in multicellularity, though see Gavrilets 2010 PLoS Comp Biol (Rapid Transition towards the Division of Labor via Evolution of Developmental Plasticity) for theoretical work.

Ulrich et al. (2018) and Tarnita et al. (2013) are now cited. We also have cited Ispolatov et al. (2012), which is relevant in this context.

[Editors' note: further revisions were suggested prior to acceptance, as described below.]

The three referees and I have read your revised manuscript, and really appreciate some of the new additions. In particular, there is a lot of enthusiasm for the new Section 5. Everyone found the paper to be thought-provoking and thought that this paper will make an important contribution to understanding ETIs if suitably revised.

The main thing we would like to suggest is a more inclusive tone for the paper. I do not think it takes away any of the novelty of the results, and indeed, can strengthen the scholarship of the work. It is critical that you revise the introduction to more fairly reflect Michod et al.'s stated meaning (not the authors' inferred meaning) about the concepts of export of fitness, fitness decoupling, and the counterfactual account. Second, the referees and I do not see why the counterfactual account is not a valid indicator that an ETI has occurred. This does not undercut the utility of your work, showing that trade-off breaking mutations can be an indication of an ETI. But all four of us are convinced that both approaches have merit.

Referee 2 has left a detailed review, highlighting five major points. The referees and I agree that it is essential to address all five points with changes to the MS, not arguments for why revision is not necessary. Please respond to their review thoroughly. I have carried forward their five summary points and provided a bit of additional context on some below, reflecting our collective post-review discussion.

Thank you for your detailed report. Our response to the comments is written in purple below. We would like to note at the outset, however, that we do not see the counterfactual account, in and of itself, as a problem. Our disagreement with the literature is limited to the concepts of export, decoupling, and transfer of fitness: we believe that the counterfactual account, while fruitful, does not satisfactorily address their limits. This response letter and the changes we have made to the manuscript aim to make this point unambiguously clear.

To address the comments from Reviewer 3 and the Reviewing Editor, we have pasted each of their five points together and responded to both in a single response (in purple below). Please find enclosed a new version of the manuscript, edited in light of your comments.

1. Adequately address Michod and colleagues' "counterfactual fitness" interpretation of their own model or give a compelling reason not to in the manuscript.

Despite pointing this out in the last revision, the paper still does not treat Michod et al.'s position on fitness decoupling and counterfactual fitness fairly. The paper is framed in such a way that it critiques a straw-man version of Michod et al's position on these topics (privileging the authors' interpretation of what Michod et al. have said, or what the metaphor of "fitness decoupling" implies), which stands in contrast to what Michod and colleagues have explicitly said they mean by these terms in their more recent papers.

Thank you for these comments, which have led us to revise the way the paper is framed. It was not at all our desire to represent ideas expressed by others unfairly. Likewise, it was not our intent to attack a strawman version of the export-of-fitness account. Rather, we aim to address this concept seriously and follow through with what it implies. We sincerely regret not having been able to convince the referee of our good faith.

We must stress that, in principle, we have no disagreement with the counterfactual approach proposed by Shelton and Michod (2014), which was already presented more implicitly in some earlier work by Michod and colleagues. However, our main contention is that it is not compatible with the ‘export-of-fitness’ account. This was stated in Line 715 of the second submission: ‘The method described by Shelton and Michod (2020), once separated from the export-of-fitness model, would prove useful here’. Here is our rationale why this is so.

The notion of counterfactual fitness stands on its own without having to be tied to fitness decoupling/transfer/export. This point can be vindicated from the work of the proponents of the counterfactual approach. In their 2014 article, Shelton and Michod mention neither fitness transfer nor fitness decoupling, thus leaving unresolved the connection between counterfactual fitness and notions of fitness decoupling, transfer or export. The same applies to the follow-up article by Leslie et al. (2017). The connection between the ‘fitness decoupling’ account and ‘counterfactual fitness’ was only later made explicit by Shelton and Michod (2020), where the authors state (in the abstract) that ‘during an ETI, fitnesses at the two levels, group and individual, become decoupled, in the sense that fitness in a group may be quite high, even as counterfactual fitness goes to zero.”

Thus, it does appear that Michod and colleagues have proposed two versions of the export-of-fitness account. To our knowledge, they have not explicitly stated that one replaced the other (however, Reviewer 3 seems to disagree on this point). Regardless of whether they have been explicit, in the interest of presenting a complete picture of the problem, we have decided to present and discuss both versions.

The earlier account was not explicit about the counterfactual nature of fitness and can be (and has been) interpreted as relating two ‘actual‘ fitnesses. We oppose this interpretation of fitness transfer/export/decoupling because actual cell and collective fitness cannot actually be decoupled, as was also appreciated by Shelton and Michod (2014). To this end, we prove mathematically that these fitnesses are equal for a wide range of models (we return to this point in the response to Essential Revision #3).

The second account explicitly refers to ‘counterfactual‘ fitness. We oppose this interpretation of fitness transfer/export/decoupling because there is no meaningful ‘transfer‘ possible between counterfactual and actual quantities. We justify this point via two arguments. First, by definition, a counterfactual fitness does not exist—thus, there is nothing material that can be transferred from a counterfactual to an actual quantity. Second, since fitness is not a conserved quantity in the model, there is no total fitness that could be distributed and transferred between potential and actual fitnesses, as is the case for energy in physics. Nevertheless, we recognise that counterfactual quantities are valuable for other purposes.

We think that making these points is not superfluous because the metaphor of fitness transfer is difficult to apply to experimental systems and has been used in inconsistent ways. In some of his most recent writings, Michod seems to agree that the straightforward interpretation of the term ‘transfer’ raises difficulties: ‘speaking of fitness “transfer” may suggest that fitness is a conserved quantity in the model which it is not’ (Michod, 2022, p44, our emphasis). As an example, when discussing fitness transfer, Shelton and Michod (2020) discuss parameters in Hamilton’s rule in the following way: ‘the evolution of altruism transfers fitness from the level of the cells to the level of the group’. They reason that this is so because the cost of altruism (C ‘units of fitness’ in Hamilton’s rule) is ‘subtracted from the cell level’ while its benefits (B ‘units of fitness’) is ‘added to members of the group’ (Shelton & Michod, 2020, p7). However, we would like to point out that the parameters C and B do not correspond to counterfactual cell and group fitness: they both appear in the expression of collective fitness (i.e., the cost C is paid in both the context of the collective and outside of it) making them de facto actual rather than counterfactual quantities.

That being said, we do agree with the reviewer that our original manuscript failed to make these points clear and could be interpreted, at times, as a rejection of counterfactual fitness in its entirety. To clarify our position, we have now reworked the Introduction to:

Present the idea of counterfactual fitness that we credit to Shelton and Michod (with mention of Michod’s earlier work, in which the idea is more implicit).
Link counterfactual fitness, following Michod and Shelton (2020), to fitness decoupling/transfer.
Recognise the general value of counterfactual fitness, but highlight the difficulty when it is used to explain fitness transfer/decoupling.

Further, in Section 1, we now provide several paragraphs presenting our rationale regarding why fitness decoupling/transfer, even if understood from a counterfactual perspective, is not adequate.

In the Discussion, we have added a section on the usefulness of counterfactual particle fitness in the context of ETIs and how it can be integrated into the tradeoff-breaking framework.

2. Make a compelling case for the lack of utility of the counterfactual fitness version of fitness decoupling in the manuscript or remove this claim from the manuscript.

Given that you are using a Darwinian Individuality approach to define what is an individual (clearly defined in the glossary, thank you!), I do not see how one can dismiss the utility of the counterfactual fitness approach. Empirical measures consistent with the counterfactual fitness account can provide insight into whether groups have been acting as Darwinian Individuals. For example, consider a lineage evolving along a pre-existing trade-off between traits that improve the fitness of groups and those that improve the fitness of cells, like those identified in Figure 8's depiction of 'optimization on the trade-off'. Using the example given in this section, consider the mutations that make snowflake yeast cells elongate, which increase group size (and thus fitness) but decrease cell growth rates (and thus fitness). This would be detected in the counterfactual fitness account and would rightly be interpreted as a trait that evolved due to selection acting among groups, not among individual cells, demonstrating that groups are Darwinian Individuals. Trade-offs have not been broken, but nonetheless, groups replicate, have heritable variation in group-level traits, and selection acts on those traits, resulting in adaptations that would not have occurred among unicellular populations. I think we can all agree that in this case, measurements consistent with the counterfactual approach would indicate that groups are a Darwinian Individual according to PGS's criteria, right? On a related note, I couldn't figure out why the MS embraced the 'Ratcheting' model but rejected the counterfactual account since ratcheting is based on the same trade-offs that would be detected by the counterfactual fitness account.

However, I think your paper raises very valid limitations on the scope of counterfactual fitness- not all multicellular adaptations will necessarily create a trade-off between fitness in groups and fitness in isolated cells, reverting lineages to unicellularity may often prove impossible, and measuring fitness can be difficult, etc. From my perspective, both the counterfactual fitness account and the trade-off breaking account may be useful indicators that an ETI (following the Darwinian Individuality criteria) has occurred. And importantly, I do not think either is necessary or sufficient to show an ETI has occurred without additional information about the traits themselves. They both require context to be informative.

Since neither is necessary for an ETI, a lineage may evolve along either route (or both simultaneously, as they are not mutually exclusive). I could imagine cases where it is much easier to identify trade-off breaking mutations and others where it is easier to identify counterfactual fitness. Having both tools available is a net positive for our field, and I don't see the need to limit ourselves only to tradeoff-breaking mutations. All the more so if trade-off breaking mutations are not necessary or sufficient to show an ETI, making the decision to only consider them somewhat arbitrary.

We wish to state again that our intention is not to dismiss the counterfactual approach. Instead, we are raising concerns regarding its interpretation in the context of the export-of-fitness (fitness transfer and decoupling) account. As mentioned in our response to the previous point, we find the idea of fitness decoupling/export/transfer inadequate in both its actual and counterfactual versions. Thus, with respect to counterfactual fitness, our main contention is with the interpretation of fitness decoupling/transfer from the counterfactual, not that the idea of counterfactual fitness can be relevant for explanation in ETIs. Our framework is compatible with both fitness decoupling and tradeoff-breaking observations and provides them a unified interpretation in terms of a tradeoff. We have reworked our manuscript to avoid suggesting that the second kind of observation should replace the first.

To ensure that our position does not come across as against the idea of counterfactual fitness, in addition to the point mentioned in the previous response, we:

Have made the point unambiguously that we find the notion of counterfactual fitness useful (throughout the manuscript).
We changed the title of Section 2.4 and reworked the paragraph.
We have also reworked the snowflake yeast example in Section 3.3, which clarifies the link between actual and counterfactual fitness.

3. Consistently describe what is and is not novel about the finding of incommensurability.

This is described clearly in the original review and I have no additional context to add.

Our work gives a general mathematical proof of the incommensurability of individual and collective fitness. It vindicates the point made previously by Shelton and Michod (2014) (‘cells and colony level fitness […] are mathematically equivalent ways of bookkeeping’(p. 457)), Bourrat (2015b) (‘during an ETI, if the fitness of the particles seems incommensurable with the fitness of the collective, it is most probably due to the fact that, during the last stage, those fitnesses are not measured over the same period of time anymore, and the interactions between particles become so complex that tracking back their fitness over longer periods of time than one or two generations appears in practice impossible’.) and Black et al. 2020 (‘within our model, this is readily explained: fitness of a cell is measured over the short timescale while patch fitness is measured over the long timescale. This captures precisely—and explains mechanistically—the notion of ‘fitness decoupling’ thought to occur during the earliest stages of the evolution of multicellular life but which has often been difficult to intuit’).

Our results are more general than the ones previously published because they do not rely on any a priori assumption regarding the relationship between collective and individual fitness, viability, and fecundity (linearity, average, tradeoff…), or on writing the model in a MLS1 or MLS2 framework. We show that in any population growth model where collective sizes reach a stable distribution, the long-term growth rates of particles and collectives are equal.

To address the reviewer’s points, we have made the following changes to the manuscript:

In the abstract, we have replaced the passage mentioned with ‘Extending and unifying results from the literature, we show that fitness of particles and collectives can never decouple because calculations of particle and collective fitness performed over appropriate and equivalent time intervals are necessarily the same provided the population reach a stable collective-size distribution’.”
Lines 95–97 have been deleted.
We have rewritten lines 109–110. We added that our work is “’generalising and unifying results from the literature” and provided references to acknowledge previous work.
Lines 190–191 have been deleted.
In Section 2.4, we have now explicitly stated the novelty of the generality of this result: ‘while these points have been made in the literature (see Section 1) our mathematical proof applies to a larger class of population dynamics models—it is not tied to a MLS1/MLS2 framework and does not require any assumptions regarding the relationship between particle and collective life history traits, such as the usual assumption that collective viability is a linear function (since the $γ$ or $μ, δ,$ and $β$ are free). It only requires that the population reaches a stable size distribution; only if the collectives are able to grow (or shrink) indefinitely, which is not a realistic assumption for ETIs, could genuine fitness decoupling be observed (see Bourrat, 2021b, Chapter 5 for details).’
Recent works by Shelton and Michod are now cited throughout the manuscript, as described in other essential revisions.

4. Consistently acknowledge that trade-off breaking is insufficient as a marker for an ETI.

As acknowledged in the prior review, trade-off breaking is not sufficient to determine that an ETI has occurred. It is possible to have a trade-off-breaking mutation occur within a single level. The referees and I agree that the MS should be consistent about this limitation and avoid saying the existence of that trade-off breaking mutations mean an ETI has occurred. To this end, it would be very helpful if the authors could identify what additional information one would need to know in order to conclude that a trade-off breaking trait indicates that an ETI has occurred (i.e., it's pretty clear if the adaptation derives from cellular differentiation in a way that overcomes cell-level trade-offs, like C and N fixation in cyanobacteria, but what about other kinds of adaptations? How would one infer that adaptations generating novel multicellular morphology are breaking trade-offs? What if the adaptations in question do not stem from the limitations of the unicellular ancestor [i.e., those that are limited by trade-offs], but rather reflect the novel ecology and behavior of the multicellular organism?).

Thank you for pointing out that we were not sufficiently clear about the role of tradeoff breakings in ETIs.

We agree that tradeoff breaking can occur within a single level. This was stated in the sentence before the one quoted by the reviewer: ‘“constraints breaking” are already considered key events in the evolution of body plans and are expected to be a widespread mechanism for the emergence of novelties’ (L 652). However, we suggest that the observation of tradeoff breaking in the context of an ETI (i.e., on traits of interest) is a relevant event that can be used as a marker of an ETI even if it is not sufficient.

Our model aims to be compatible with both fitness decoupling and tradeoff-breaking observations. We have reworked our manuscript to avoid suggesting that the second kind of observation should replace the first; rather, it should come at a later stage of the transition (phase 3 instead of phase 2 in Figure 8).

Regarding the operationalisation of the concept, please note that, in our framework, the tradeoff-breaking mutation is an abstract phenotypic change that could, in principle, be due to ecology, behaviour, or plasticity, in addition to genetic mutations. Developing a general method to select relevant traits and detect tradeoff breaking in any transition in individuality moves beyond the scope of the present manuscript, but is a promising avenue for future research.

To clarify these points and address the comments from the Reviewer and Reviewer Editor, we have:

Changed the sentence in the Abstract (line 42) from “tradeoff-breaking stands as a useful marker for ETIs” to “Thus, when observed in the context of ETIs, tradeoff-breaking events stand as a useful marker for these transitions.”
Changed the sentence on line 537 from “… tradeoff-breaking observations are the mark of significant genetic innovation and, thus, can be used as a hallmark of ETIs,” to “as we advocate that such tradeoff-breaking observations in this context are the mark of significant innovation and, thus, can be used to detect ETIs.”
Changed the sentence in lines 417–418 from “…one genuine marker for an ETI is the capacity for a lineage to break away from such a tradeoff," to “the capacity for a lineage to break away from such a tradeoff could be used to detect an ETI.”
Lines 669–670 have been rewritten and now read as: “Finally, we propose that rare tradeoff-breaking events are a crucial part of ETIs and could be used experimentally for their detection.”
Lines 687–689 now read: “Our second main result is a general adaptive scenario of ETIs that is compatible with both experimental fitness-decoupling observations (artifactual or counterfactual) and tradeoff-breaking deviations.”
Given more context throughout the manuscript and following the response to the previous comments regarding why tradeoff breaking can be a marker for an ETI.
In Section 5, we have:
- Italicised “in and of itself” in the sentence: “Thus, a tradeoff-breaking event in and of itself cannot be used as a marker of an ETI.”
- Contextualised our claims in the following: “However, considering a trait in the context of an ETI, where collectives are formed and maintained (phases 1 and 2) and establishing how those collectives change and potentially overcome the constraints that historically bear on particles (phase 3) offers a good empirical handle to study ETIs. Conversely, the lack of any tradeoff-breaking observation in such an empirical system could be used as an indication that the transition is still in its early stages.”

To answer specifically regarding the other information necessary for an ETI, we would need to have clearly identified discrete higher-level entities (or entities in the process of discretisation), what Clarke (2013) calls “mechanisms of demarcation.” We now mention this in Section 5.
Finally, to clarify the scope of the tradeoff-breaking model, we have included a sentence at the beginning of Section 3 stating that we consider mutations to be abstract changes in phenotype that could potentially be induced by environmental changes (on top of genetic mutation and phenotypic plasticity).

5. Clarify, in the manuscript, how the dynamics of F and f2 fail to explain the dynamics described in lines 407-417.

This is described clearly in the original review and I have no additional context to add.

There seems to be disagreement between us and Reviewer 3 regarding what constitutes an explanation of dynamics. We do not think that the relative dynamics of F and f2 explain the evolutionary dynamics of the system because there is no actual causal link between the dynamic of the counterfactual fitness f2 and the actual evolutionary dynamics. The value of f2 is entirely irrelevant to the dynamics of trait values. Starting from a given initial condition (i.e., initial trait value), the trait would have the same dynamics whether f2 decreases, increases, or even oscillates. The only quantity that matters and explains the trait changes is the gradient of F.

Now, measuring the counterfactual fitness f2 might be of interest, but not because its dynamics relative to F explain anything about the dynamics of the trait value theta (e.g., through some putative transfer mechanism)—rather, because it gives us a hint that there might be a tradeoff here between traits that contribute to collective fitness or would contribute to counterfactual cell fitness.

Once again, our point is that the counterfactual fitness approach is valuable, but only when taken for what it is: a counterfactual, and not what it is not (and what it cannot be)—that is, something to be transferred to F. Using it in the context of export-of-fitness is inconsistent, as we have argued in the previous points.

We have edited line 407–417 to reflect this (this also partly addressed Essential Revision #2). We made a reference to this paragraph in Section 2.4 when we discuss the general usefulness of fitness-decoupling observations.

Reviewer #2 (Recommendations for the authors):

Recommendations for authors

These have a 1:1 correspondence with the items above

1. Adequately address Michod and colleagues' "counterfactual fitness" interpretation of their own model or give a compelling reason not to in the manuscript.

This is now done in the Introduction, Section 1, and the Discussion.

2. Make a compelling case for the lack of utility of the counterfactual fitness version of fitness decoupling in the manuscript or remove this claim from the manuscript.

We have now clarified the link between counterfactual fitness and fitness decoupling/transfer, and why counterfactual fitness does not provide a satisfactory account of fitness decoupling. However, we have stressed that the concept of counterfactual fitness, in and of itself, can be useful in the context of ETIs.

3. Consistently describe what is and is not novel about the finding of incommensurability.

We have now clarified, from the abstract onwards, what is novel about our result.

4. Consistently acknowledge that trade-off breaking is insufficient as a marker for an ETI.

We have now done so.

5. Clarify, in the manuscript, how the dynamics of F and f2 fail to explain the dynamics described in lines 407-417.

These lines have been rewritten.

Reviewer #3 (Recommendations for the authors):

I really enjoyed reading the revised manuscript, especially the newly-added Section 5. I think everything is much clearer now, and although parts and ideas have been discussed elsewhere, bringing them together in a coherent conceptual and theoretical framework is novel and useful. It certainly got me thinking in directions that I hadn't previously considered.

I have only one final comment. I appreciate the idea of separating the stage of collective formation from the subsequent ones and the authors' clarification that they focus on the latter (and hence that they choose not to focus on the competition with unicellular ancestors). But what if some collective property is needed precisely to overcome the competition with the unicellular ancestor? That's certainly how the experiments in Ulrich et al. 2018 came about: because in a model similar to the one in Tarnita et al. 2013 but published in the context of eusociality in Nowak et al. 2010, we predicted that a necessary condition for eusociality to evolve was for per capita fitness to get a drastic boost at very small, incipient group sizes, without any time for additional mutations. And in 2010 we had no clue what that could be. In 2018 we showed experimentally that spontaneous, rudimentary division of labor could do it.

In other words, one might sometimes be in a situation where Stage 2 is altogether skipped precisely because only collectives that snap right into some form of Stage 3 already during stage 1 can outcompete the ancestor. Put differently, Stage 1 = Stage 3.

Again, it seems to me that there are many ways to skin a cat and the authors are making it clear now that rare mutation doesn't have to be the only route to an ETI, but that some overarching framework based on traits and tradeoffs might offer a more productive way to look broadly at ETIs. I just wanted to alert them to the possibility that tradeoff breaking might not necessarily always occur after Stage 1 (and the associated competition with the ancestor) but sometimes might even occur during it. Unless I'm missing something?

Thank you for your feedback—we are glad that our revisions added clarity. We agree that Stage 2 can be skipped. This is included in Figure 8 as Route 2 and also in the section on the importance of phenotypic plasticity for a primordial form of division of labour. We have modified the relevant part of Section 5 to clarify that Stage 3 can immediately follow Stage 1.

It must be noted that since the focus of this article has been predominantly on fitness-decoupling observations, we have explained Route 1 in more detail. Nevertheless, Route 2 is very interesting and might, in fact, be widespread in nature.

https://doi.org/10.7554/eLife.73715.sa2

Article and author information

Author details

Pierrick Bourrat
1. Philosophy Department, Macquarie University, Sydney, Australia
2. Department of Philosophy & Charles Perkins Centre, The University of Sydney, Sydney, Australia
Contribution
Conceptualization, Funding acquisition, Methodology, Writing – original draft, Writing – review and editing

Contributed equally with
Guilhem Doulcier

For correspondence
p.bourrat@gmail.com

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0002-4465-6015
Guilhem Doulcier
1. Philosophy Department, Macquarie University, Sydney, Australia
2. Department of Evolutionary Theory, Max Planck Institute for Evolutionary Biology, Plön, Germany
Contribution
Conceptualization, Formal analysis, Software, Visualization, Writing – original draft, Writing – review and editing

Contributed equally with
Pierrick Bourrat

For correspondence
guilhem.doulcier@normalesup.org

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0003-3720-9089
Caroline J Rose

Centre d'Écologie Fonctionnelle et Évolutive (CEFE), CNRS, Montpellier, France

Contribution
Conceptualization, Writing – review and editing

Competing interests
No competing interests declared
Paul B Rainey
1. Laboratoire Biophysique et Évolution, CBI, ESPCI Paris, Université PSL, CNRS 75005 Paris, France, Paris, France
2. Department of Microbial Population Biology, Max Planck Institute for Evolutionary Biology, Plön, Germany
Contribution
Conceptualization, Writing – review and editing

Competing interests
Reviewing editor, eLife

"This ORCID iD identifies the author of this article:" 0000-0003-0879-5795
Katrin Hammerschmidt

Institute of Microbiology, Kiel University, Kiel, Germany

Contribution
Conceptualization, Data curation, Writing – original draft, Writing – review and editing, Funding acquisition

For correspondence
katrinhammerschmidt@googlemail.com

Competing interests
No competing interests declared

"This ORCID iD identifies the author of this article:" 0000-0003-0172-8995

Funding

John Templeton Foundation (62220)

Pierrick Bourrat
Katrin Hammerschmidt
Guilhem Doulcier

Max Planck Institute for Evolutionary Biology (Open access funding)

Paul B Rainey
Guilhem Doulcier

Australian Research Council (DE210100303)

Pierrick Bourrat

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank María Rebolleda-Gómez, Matthew Herron, Corina Tarnita, and Will Ratcliff for review of the manuscript and valuable comments. We also thank the Theory & Method in Biosciences group at the University of Sydney and Macquarie University, for their feedback on a previous version of the manuscript. Finally, we thank Sarah Pearce for editing the mansuscript.

Senior Editor

Patricia J Wittkopp, University of Michigan, United States

Reviewing Editor

Will Ratcliff, Georgia Institute of Technology, United States

Reviewers

María Rebolleda-Gómez, University of California, Irvine, United States
Matthew Herron, Georgia Institute of Technology, United States
Corina E Tarnita, Princeton University, United States

Publication history

Preprint posted: September 2, 2021 (view preprint)
Received: September 8, 2021
Accepted: June 28, 2022
Accepted Manuscript published: August 17, 2022 (version 1)
Version of Record published: September 13, 2022 (version 2)

Copyright

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.